Question

100 POINTS!!!!!!!! Use the linear combination method to solve the system of equations. Be sure to show all your steps in the space below.

-3x+8y=16
X-4y=-12

Answer 1

To solve the system of equations -3x+8y=16 and x-4y=-12 using the linear combination method, we want to eliminate one of the variables by multiplying one or both equations by a constant.

hope this helps!

In this case, if we multiply the second equation by 3, we can eliminate x by adding the two equations together.

Original equations:
-3x+8y=16
x-4y=-12

Multiplying the second equation by 3:
-3x+8y=16
3x-12y=-36

Adding the two equations together:
-3x+8y=16
+3x-12y=-36
-------------
-4y=-20

Solving for y, we get:
-4y/-4 = -20/-4
y = 5

Now that we know y=5, we can substitute this value into one of the original equations to solve for x. Let's use the second equation:
x-4y=-12
x-4(5)=-12
x-20=-12
x=-12+20
x=8

Therefore, the solution to the system of equations -3x+8y=16 and x-4y=-12 is x=8 and y=5.

Answer 2

The solution to the given system of equations is x = 8 and y = 5.

Step-by-step explanation:

The linear combination method is a technique used to solve a system of linear equations.

To use the linear combination method, multiply one (or both) of the equations by a constant so that when the two equations are added or subtracted, one of the variables will be eliminated.

Given system of linear equations:

`\begin{cases}-3x+8y=16\\ x-4y=-12\end{cases}`

Multiply the second equation by 2 so that the coefficient of the y variable is equal in magnitude but has the opposite sign to the coefficient of the y variable in the first equation, i.e. 8y:

`\implies 2(x-4y)=2(-12)`

`\implies 2x-8y=-24`

Add this to the first equation to eliminate the y variable:

`\begin{array}{crcccr}&-3x & + & 8y & = & 16\\+&(2x&-&8y&=&-24\\\cline{2-6}&-x&&&=&-8\end{array}`

Solve for x by dividing both sides by -1:

`\implies (-x)/(-1)=(-8)/(-1)`

`\implies x=8`

Now that we have solved for x, we can substitute x = 8 back into one of the original equations to solve for x.

Substitute x = 8 into equation 2 and solve for y:

`\implies 8-4y=-12`

`\implies 8-4y-8=-12-8`

`\implies -4y=-20`

`\implies (-4y)/(-4)=(-20)/(-4)`

`\implies y=5`

Therefore, the solution to the given system of equations is x = 8 and y = 5.