Question

Which ordered pair is a solution to the system of linear equations?

2x + 3y= 6

–3x + 5y = 10

(0,2)
(2,0)
(3,2)
(2,3)

Answer 1

We have to add the equations in a clever way such that one of the variables cancels out. If you multiply the top one with 3 and the bottom one with 2, you cancel x. Like this:

3(2x+3y)=3*6 => 6x + 9y = 18
2(-3x+5y)=2*10 => -6x + 10y = 20

9y + 10y = 38 => 19y = 38 => y=2

If y=2 then 2x + 6 = 6 => x=0

The pair (0,2) is a solution.

Answer 2

(0,2)............................................