Question

How do you solve `x + y = -4` and `y = -3x + 2` using substitution?

Answer 1

`x=3`
`y=-7`

Explanation:

Given equations are
`x+y=-4" "`first equation
`y=-3x+2" "`second equation

Substitute the second equation to the first equation

`x+y=-4" "`first equation
`x+(-3x+2)=-4" "`first equation

`x-3x+2=-4`

`-2x=-4-2`

`-2x=-6`

divide both sides of the equation by `-2`

`(-2x)/(-2)=(-6)/(-2)`

`(cancel(-2)x)/cancel(-2)=(-6)/(-2)`

`x=3`

Use the second equation and `x=3`

`y=-3x+2" "`second equation
`y=-3(3)+2" "`second equation

`y=-9+2`
`y=-7`

God bless....I hope the explanation is useful.

Answer 2

`x=3`
`y=-7`

Explanation:

Let's make
`x+y=-4` equation 1

`y=-3x+2` equation 2

The substitution method means that you will take an equation and plug it into another one to get rid of an unknown.

These questions may sometimes require you to rearrange one of the equations first, so that there is only one variable* on one side of the equation.

In this case, that won't be necessary as equation 2 is already in this form. There is only the variable y on the left side.

Now, you can look at equation 1 and ask yourself where you can plug equation 2 into.

`x+y=-4`

We can see that the y can be replaced with -3x+2 since they are both equal.

`x+ (-3x+2) = -4`
`x-3x+2=-4`
`x-3x=-4-2`
`-2x=-6`

`x=(-6)/-2`

`x=3`

Now we know that `x=3`, we can plug that into any of the 2 equations to find y. I'll use equation 1.

`x+y=-4`
`3+y=-4`
`y=-4-3`
`y=-7`

Conclusion:
`x=3 , y = -7`

# A variable is a number we don't know yet which is represented by a letter such as x or y.