Question

Please help me with this question that were stuck on I am trying to help my son to understand but I am having trouble with breaking this down. He brought it back home from getting it wrong please help. I have attached a picture of the problemUse the linear combination method to solve the system of equations. Explain each step of your solution.2x – 3y = 133x + y = -8

Answer 1

The given equations are

`2x-3y=13\text{ take it as equation (1).}`
`3x+y=-8\text{ take it as equation (2).}`

We need to eliminate one variable by adding and subtracting the equations.

First, multiply equation (1) by 3 as follows.

`3*2x-3*3y=3*13\text{ }`

`6x-9y=39\text{ take it as equation (3).}`

Multiplying equation (2) by (-2) , we get

`(-2)3x+(-2)y=-(-2)8`

`-6x-2y=16\text{ take it as equation (4).}`

Add equation (3) and equation (4) to eliminate the x variable.

`(6x-9y)+(-6x-2y)=39+16`

`6x-9y-6x-2y=39+16`

`-11y=55`

Dividing both sides by (-110, we get

`-(11y)/(-11)=(55)/(-11)`
`y=-5`

We get y=-5.

Substitute y=-5 in the equation (1), to find the value of x.

`2x-3(-5)=13`

`2x+15=13`

Subtracting 15 from both sides of the equation, we get

`2x+15-15=13-15`

`2x=-2`

Dividing both sides by 2, we get

`(2x)/(2)=-(2)/(2)`
`x=-1`

Hence the solution is

`x=-1\text{ and }y=-5`