Question

How do you solve `y = -x + 5` and `2x - 3y = -6` using substitution?

Answer 1

`(9/5,16/5)`

Explanation:

As given by the first equation, we see that `color(red)(y=-x+5)`. Because of this, we can plug `color(red)(-x+5` in for `color(red)y` in the second equation.

`2x-3color(red)y=-6" "=>" "2x-3(color(red)(-x+5))=-6`

When distributing `-3` into `(-x+5)`, note that the negative will change the signs of the terms in the parentheses, so:

`-3(color(blue)-xcolor(blue)+5)=color(green)+3xcolor(green)-15`

So, we have

`2x+3x-15=-6`

`5x-15=-6`

`5x=9`

`color(purple)(x=9/5`

With this, we can plug this value for `x` into either equation. I'll choose the first, since it's simpler:

`y=-color(purple)x+5" "=>" "y=-color(purple)(9/5)+5`

Find a common denominator:

`y=-9/5+25/5`

`color(brown)(y=16/5)`

Since we have `color(purple)(x=9/5` and `color(brown)(y=16/5)`, our final answer is the ordered pair `(color(purple)(9/5),color(brown)(16/5))`.