Question

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

Answer 1

It can be solved either by substitution or by elimination.

1) Substitution: `x-2y=8 \Rightarrow x=2y+8\Rightarrow -(2y+8)+3y=-5`

`\Rightarrow y=3\Rightarrow x=6+8=14` and the unique answer is the point `(x,y)=(14,3)`.

2) Elimination: add the two equations to get `y=3` and then substitute into, for example, the second equation to get `x=3y+5=9+5=14` so that the unique answer is the point `(x,y)=(14,3)`.