Question

How do you solve the simultaneous equations `y = -2x + 10` and `3x + 5y = 8`?

Answer 1

`(x,y) = (6,-2)`

Explanation:

[1]`color(white)("XXXX")` `y = -2x+10`
[2]`color(white)("XXXX")` `3x+5y = 8`

Substituting `(-2x+10)` for `y` (from [1]) in [2]
[3]`color(white)("XXXX")` `3x +5(-2x+10)=8`
Simplifying
[4]`color(white)("XXXX")` `7x = 42`
[5]`color(white)("XXXX")` `x = 6`

Substituting `6` for `x` back in [1]
[6]`color(white)("XXXX")` `y = -2(6)+10`
[7]`color(white)("XXXX")` `y = -2`