Question

Use the linear combination method to solve the system of equations.

Explain each step of your solution. If steps are not explained, you will not
receive credit for that step.
2 + 9 = −26
−3 − 7 = 13

Answer 1

Given the system of equation:

`2x+9y = -26` .....[1]

`-3x-7y=13` ......[2]

Multiply equation [1] by -3 to both sides we get;

`-6x-27y = 78` .....[3]

Multiply equation [2] by 2 to both sides we get;

`-6x-14y = 26` .....[4]

Subtract equation [4] from [3] to eliminate x we get;

`-6x-27y-(-6x-14y) = 78-26`

`-6x-27y+6x+14y= 78-26`

Combine like terns we get;

`-13y = 52`

Divide both sides by -13 we get;

y = -4

Substitute the value of y in equation [1] we get;

`2x+9(-4) = -26`

`2x-36 = -26`

Add 36 to both sides we get;

2x = 10

Divide both sides by 2 we get;

x = 5

Therefore, the solution for the system of equation is (5, -4)