Question

How do you solve by substitution `3y=-1/2x+2` and `y=-x+9`?

Answer 1

For the given equations, `(x,y) = (10,-1)`

Explanation:

[1]`color(white)("XXXX")` `3y = -1/2x+2`
[2]`color(white)("XXXX")` `y = -x +9`

While it is not technically necessary, I find it easier to clear the fractions before actually beginning; so multiplying [1] by `2`
[3]`color(white)("XXXX")` `6y = -x+4`

Substituting (from [2]) `(-x+9)` for `y` in [3]
[4]`color(white)("XXXX")` `6(-x+9) = -x+4`

Simplifying
[5]`color(white)("XXXX")` `-6x+54 = -x+4`
[6]`color(white)("XXXX")` `5x = 50`
[7]`color(white)("XXXX")` `x=10`

Substituting (from [7]) `10` for `x` in [2]
[8]`color(white)("XXXX")` `y = -10 +9 = -1`