Question

How do you solve the system `x+2y=13` and `-2x-3y=-18` using substitution?

Answer 1

`x=-3` and `y=8`

Explanation:

Starting with `x+2y=13`, get `x` by itself on the left-hand side by subtracting `2y` from both sides.

`x=-2y+13`

This gives us a new name for `x`, which we can plug back in to

`-2color(red)(x)-3y=-18`

`-2(color(red)(-2y+13))-3y=-18`

`4y-26-3y=-18`

Combine the terms with `y`

`y-26=-18`

Add `26` to both sides.

`y=8`

Now plug `y=8` back into one of the two equations with both `x` and `y` still in it from above.

`x=-2color(red)(y)+13`

`x=-2(color(red)(8))+13`

`x=-16+13`

`x=-3`

ANSWER: `x=-3` and `y=8`

Answer 2

`x = -3`

`y = 8`

Explanation:

Since,

`x + 2y = 13`

Then,

`x = 13 - 2y`

Substuting `[x = 13 - 2y]` in the other equation, `(-2x - 3y = -1)`, It becomes

`-2(13 - 2y) - 3y = -18`

Simplify,

`-26 + 4y - 3y = -18`

Which is the same as:

`-26 + y = -18`

Put `y` on the left side of the equal sign and actual numbers on the right

`y = -18 + 26`

`y = 8`

Go back and solve `[x = 13 - 2y]` for `x`, since you now know what `y` is:

`x = 13 - 2(8)`

`x = 13 - 16`

`x = -3`

Ta da! Please do correct if I'm wrong...
Cheers and all the best!