Question

How do solve the following linear system?: `5x+2y=4 , y=-3x+4`?

Answer 1

`x=4, y=-8`

Explanation:

`5x+2y=4`
`y=-3x+4`

Since the second function already has the y term isolated, plug it in for y in the first function to solve for x

`5x+2(-3x+4)=4` (Distribute the 2)

`5x-6x+8=4` (Combine like terms)

`-x+8=4` (Subtract 8 from both sides)

`-x=-4` (Divide both sides by -1)

`x=4`

Now that you found the x variable, plug it into either equation to find y

`y=-3(4)+4` (Distribute -3)

`y=-12+4` (Find the difference/sum)

`y=-8`

Check your answer by plugging it back into either of the original equations

`5(4)+2(-8)=4`

`20+(-16)=4`

`4=4`

This is how you solve by substitution