please help me with this system of equations problem before I go insane the preferable solving methods would be through substitution or elimination
Answers
Answer:
x=8, y=0, z=-3
Step-by-step explanation:
Preferable is substitution because there is less room for mistakes but its long so here goes bare with me on this one :D
Name your equations
4x+2y-5z=47 (first eq)
x-2y+6z=-10 (second eq)
9x-7y-z=75 (third eq)
Lets take the easiest eq to isolate one variable lets take 2nd eq
[tex]x-2y+6z=-10\\x=2y-6z-10[/tex]
now this becomes our fourth eq
now again take the easiest eq to isolate another variable lets take the 3rd eq
[tex]9x-7y-z=75\\9x-7y-75=z[/tex]
now this becomes our fifth eq
and now plug in our fifth eq in the fourth eq because we now have z in terms of x and y
[tex]x=2y-6z-10\\x=2y-6(9x-7y-75)-10\\x=2y-54x+42y+450-10\\x+54x=2y+42y+450-10\\55x=44y+440\\\\x=\frac{44y+440}{55}[/tex]
and now we got our sixth equation which is x only in terms of y.
now we plug in our sixth equation in our fifth eq to get z in terms of y only
[tex]z=9x-7y-75\\\\z=9(\frac{44y+440}{55}) -7y-75\\z=\frac{396y+3960}{55} -7y-75\\z=\frac{396y+3960-385y-4125}{55} \\z=\frac{11y-165}{55}[/tex]
now we have our seventh eq and x &z in terms of just one variable y , now we put equation of z and x which is our sixth eq and seventh eq in our first eq.
[tex]4x+2y-5z=47\\\\4(\frac{44y+440}{55})+2y-5(\frac{11y-165}{55}) =47\\\\\frac{176y+1760}{55} +2y-47=\frac{11y-165}{11} \\\\\frac{176y+1760}{55} -\frac{11y-165}{11} -47=-2y\\\\\frac{176y+1760}{55}-(y-15) -47=-2y\\\\\frac{176y+1760}{55} -y-32=-2y\\\\\\frac{176y+1760}{55}=-2y+y+32 \\\\176y+1760=55(-y+32)\\176y+1760=-55y+1760\\176y-55y=1760-1760\\121y=0\\y=0[/tex]
and now finally we got y=0 now we need the value of x and z, put the value of y=0 in our seventh eq (z equation)
[tex]z=\frac{11y-165}{55} \\\\z=\frac{11(0)-165}{55} \\\\z=\frac{-165}{55}\\\\z=-3[/tex]
and now we put the value of y=0 in our sixth eq (x equation)
[tex]x=\frac{44y+440}{55} \\\\x=\frac{44(0)+440}{55} \\\\x=\frac{440}{55} \\\\x=8[/tex]
and now we got all the three values and hence the solution of the system of equation is
x=8, y=0, z=-3
Related Questions
Please help i’m having a hard time answering it
Answers
4x5=20ft
6x5=30ft
A local mechanic charges customers a flat fee of $60 before any work is done in the rate of 85 per hour for labor which equation represents the relationship between the total charge for labor L in dollars and the number of hours worked h?
Answers
Answer:
im not sure but here u go 85x+60
Which rule describes the transformation?
Answers
I think its (x,y-(-x,-y)
help please !!!!! no explanation needed
Answers
Answer:
Its D super easyyyyyyhWhat is 13 / 143 as a unit fraction
Answers
Answer:1/11
Just got it using some brain cells >:)
Answer:
1/11
Step-by-step explanation:
13/143=1/11
what is the translation of the expression 5 more than twice x
Answers
Answer:
5+2x
Step-by-step explanation:
Answer:
5 + 2x
Step-by-step explanation:
Nine years ago, Tarah opened a savings account with her bank. She started with a balance of $359 and has not made any withdrawals or deposits since then. If her interest rate is 8% each year, how much interest has accrued using simple interest?
Total Interest = $
What is Tarah's new total balance?
New Balance Total = $
Answers
Answer:
Total interest = $28.72
New balance = $ 387.72
Explanation: Tarah has $359 in the bank. To find the amount of interest, multiply 359 by .08.
She gets $28.72 interest annually.
In one year, she will make $387.72. (Add the total interest to her original balance)
Plz mark brainliest:)
Janelle would like to give a party bag to every person who is coming to her party. The cost of the party bag is $7 per person. Write an inequality that describes the number of people P that she can invite if Janelle has No more than $95 dollars to spend on the party bags.
Answers
Answer: Inequality that describes the number of people P that she can invite if Janelle has No more than $95 dollars to spend on the party bags: 7P ≤ 95
Step-by-step explanation:
Given: The cost of the party bag is $7 per person.
P represents the number of people that she can invite.
Total cost for P people = ( cost per person) x (P)
=$ 7P (i)
If Janelle has No more than $95 dollars to spend on the party bags.
That means , Total cost ≤ $ 95
From (i)
7P ≤ 95 , which is the required inequality.
Which sequence of transformations will result in a parallelogram with vertices A(−2, 1), B(−4,−3), C(2,−5), D(4,−1) being carried onto the parallelogram A'B'C'D' shown below?
Answers
Answer:
translated 1 unit right and 2 units up followed by a reflection across x axis
Step-by-step explanation:
Parallelogram has vertices A(−2, 1), B(−4,−3), C(2,−5), D(4,−1) while parallelogram A'B'C'D' has vertices A'(-1, -3) B'(-3, 1) C'(3, 3) D'(5, -1)
Transformation is the movement of a point from its initial location to new location. If an object is transformed then all its points are transformed. Types of transformation are rotation, reflection, dilation and translation.
If a point X(x, y) is translated a units right and b unit up , the new point is X'(x + a, y + b).
If a point X(x, y) is reflected across the x axis, the new point is X'(x, -y)
If parallelogram ABCD is translated 1 unit right and 2 units up (i.e. x + 1, y + 2), the new points is A*(-1, 3), B*(-3, -1), C*(3, -3), D*(5, -1). If a reflection across x axis is then done, the new point is A'(-1, -3) B'(-3, 1) C'(3, 3) D'(5, -1)
Answer:
A translation 1 unit right and 2 units up followed by a reflection across the x-axis.
Step-by-step explanation:
Because you slid the shape over.
Hope this helps! Stay safe! :))))HELP ME PLS one bottle of shampoo costs 6 dollars for 8 Oz a second bottle costs 4 dollars for 5oz of shampoo wich has a lower unit rate and how much lower
Answers
Answer:
The 8 oz has lower unit rate, it's lower by .2.
Step-by-step explanation:
8 oz divided by $6 = $1.333 for 1 oz ---- (round to 1.3)
6 oz divided by $4 = $1.5 for 1 oz
10points!
will make brainliest for correct answer
-8 1/3 + (- 1/6)
Answers
Answer:
-8 1/2
Step-by-step explanation:
-8 1/3 + (- 1/6)
Get a common denominator
-8 2/6 - 1/6
Combine terms
-8 3/6
Simplify
-8 1/2
The value of -4 - x is positive. What must be true about x ?
i need help with this asap
Answers
Answer:
x must be less than -4Step-by-step explanation:
We need to set the equation equal to 0
-4 - x > 0
+ -4 + -4
x < - 4I need help with this asap
Answers
Answer:
3\sqrt{3}
Step-by-step explanation:
look this up and it will give you the answer
pls mark brainliest
Answer:
The sqrt of 3 is an irrational number.
The sqrt of 9 is a rational number.
Step-by-step explanation:
Noah’s dog weighs 15 1⁄3 pounds (lbs). Aiden’s dog weighs three times as much as Noah’s. How many pounds does Aiden’s dog weigh?
Answers
===============================================
Work Shown:
N = weight of Noah's dog = 15 & 1/3 pounds
A = weight of Aiden's dog = unknown
A = 3*N
A = 3*(15 & 1/3)
A = 3*(15 + 1/3)
A = 3*15 + 3*(1/3) .... distribute
A = 45 + 1
A = 46
Aiden's dog weighs 46 pounds.
How do I solve |x-1|-1.4 = 6.2
Answers
Answer:
x1= -6.6 x2= 8.6
Step-by-step explanation:
Answer:
x1= -6.6, x2= 8.6
Step-by-step explanation:
|x-1|-1.4=6.2
|x-1|=6.2+1.4
|x-1|= 7.6
x-1=7.6 or x-1= -7.6
x= 8.6 and x= -6.6
Find the x - and y - intercepts of the graph of the linear equation-4x+8y=-16
Answers
Answer:
y-intercept: (0, -2)
x-intercept: (4, 0)
Step-by-step explanation:
The x intercept occurs when y = 0, so you can substitute 0 in for y and solve for x as shown:
-4x+8y=-16
-4x+8(0)=-16
-4x+0=-16
-4x=-16
x=4 ---------- format correctly in (x, y) : (4, 0)
The y intercept occurs when x = 0, so you can substitute 0 in for x and solve for y as shown:
-4x+8y=-16
-4(0)+8y=-16
0+8y=-16
8y=-16
y=-2 ---------- format correctly in (x, y) : (0, -2)
hi, can someone please answer this?
Answers
Step-by-step explanation:
[tex] \frac{7}{27} [/tex]
it helps you ☺️☺️
Thank you ☺️☺️
Write the equation of a line that passes through the point (3, 4) and has a slope of -1
Answers
Answer:
[tex]Y = -1x + 4[/tex]
Step-by-step explanation:
Hope this helps
how do i put 5x^2+6+3xy^5-2x in standard form
Answers
Answer:
it's 3xy^5 + 5x^2 -2x +6
a little boy gets a haircut.the total cost is $24 and the tip should be 10% how much should the barber get as a tip?
Answers
Answer:
2.40$ or 2.4$
Step-by-step explanation:
divide 24 and 10 and you should get the answer of 2.40$ or 2.4$
please help im struggling really bad on this one question.
Answers
Answer:
B
Step-by-step explanation:
90 degrees means 1/4 of 360 degrees. If you think about it like a clock it would be at 3:00. B is the representation of that
Answer:
B
Is going clock wise I dont really know how to explain it
Geometry Question: Image is provided below.
Please show all work and your steps.
25 points
Answers
We can simplify that into 18x + 54 = 180
Now we take away 54 from both sides to get 18x = 126
Now divide both sides by 18 and we get
x = 7.
Now that we know that x = 7 we know that the 10x + 54 angle is equal to 124 by substituting the value of x in. We also know that 11y + 14 must equal to 124 because of vertically opposite angles. So we have 11y + 14 = 124.
Take away 14 from both sides; 11y = 110
Now divide both sides by 11 and we get
y = 10
So x = 7 and y = 10
I hope that you understood all of my steps and if this did help you a Brainliest would be very appreciated :)
Answer:
x=7
y=10
Step-by-step explanation:
8x and 11y+14 are same side interior angles so they add to 180 degrees
11y+14 and 10x+54 are vertical angles so they are equal
8x + 11y+14 = 180
11y+ 14 = 10x+54
Substitute 10x+54 for 11y+14 in the first equation
8x +10x+54 = 180
Combine like terms
18x+54 =180
Subtract 54
18x+54-54=180-54
18x =126
Divide by 18
18x/18 = 126/18
x=7
Now we can find y
11y+ 14 = 10x+54
11y + 14 = 10*7+54
11y+14 = 70+54
11y+14 =124
Subtract 14 from each side
11y = 124-14
11y =110
Divide by 11
11y/11=110/11
y =10
no fake answers please easy question You are solving systems of equations by graphing and you get the following graph shown below? What is the solution to this system? How do we know what the solution of a system is when graphing?
(4 sentences at least_
Answers
Answer:
Hi There! There are no solutions to this system.
Step-by-step explanation:
nd When graphing a set of equations, make sure that the slopes are not equivlient. If the slopes are equivlient, the lines are parallel, and parallel lines do not intersect. You can check the slope of the equations to find if they are equal. Both graphs go down by 3 each time they go over 2, making the slope -3/2. If they have the same slope, but a diffrent Y interset, they are parallel. You can also set the equations equal to each other, and when solving find that 7 does not equal 1, or
-3/2X+7=-3/2X+1
+3/2X
7=1
Because this is false, the lines will not intersect.
How do I solve this?(tangent segment)
Answers
Answer:
x = 6
Step-by-step explanation:
Given a tangent and a secant from an external point to the circle, then
The square of the tangent is equal to the product of the measures of the external part and the entire secant, that is
x² = 4(4 + 5) = 4 × 9 = 36 ( take the square root of both sides )
x = [tex]\sqrt{36}[/tex] = 6
Neptune is 2,798,842,000 miles from the sun. How many hours does it take lightto travel from the sun to Neptune?
Answers
9514 1404 393
Answer:
4.17 hours
Step-by-step explanation:
The speed of light is about 670,616,629.4 miles per hour, so the travel time to Neptune is ...
(2,798,842,000 mi)/(670,616,629.4 mi/h) ≈ 4.17 h
It takes about 4.17 hours for light to travel from the sun to Neptune.
The ratio of adult cats to kittens at a pet care center on was 5:2 . There were 12 kittens there that day. Thursday , 38 adult cats were at the pet care center. What is the difference between the number of adult cats at the pet care center on thursday and monday?
Answers
Answer:
8 adult cats
Step-by-step explanation:
The ratio of adult cats to kitten at the pet care center was 5:2
No of adult cats= 5x
No of kitten cats= 2x
Since there were 12 kittens that day
2x= 12
x= 12/2
x= 6
Number of adult cats = 5x
= 5 × 6
= 30 adult cats
Therefore since there were 38 adult cats in the pet center in Thursday then the difference between the number of adult cats in Thursday and Monday can be calculated as follows
= 38-30
= 8 adult cats
simplest radical form
-5√243-3√27
Answers
Answer:
-54√3
Step-by-step explanation:
What is the volume of the cylinder below
Answers
Answer:
I think d or b
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
ASAP!!! PlEASE !!!!!!!!!
Answers
Answer:
100 yards cubed
Answer: 100
Step-by-step explanation:
multiply them all together
A submarine dives below the surface, heading downward in four moves. If each move downward was 235
feet, where is the submarine after it is finished diving?
The submarine would be
feet below sea level, or
feet.
Answers
Answer:
Step-by-step explanation:
It drops 235 feet per move.
235 * 4 = 1140 feet below sea level.
-1140 is also possible.