3x + 5y=21, 2x + 3y=13
6 x + 10 y = 42 two times it
6 x + 9 y = 39 three times it
--------------------- subtract
0 x + 3 y = 3
looks like y =1
go back and find x
There are several methods for solving systems of linear equations.
This is one of them.
3 x + 5 y = 21
-
2 x + 3 y = 13
___________
3 x - 2 x + 5 y - 3 y = 21 - 13
x + 2 y = 8
Subtract 2 y to both sides
x = 8 - 2 y
Put this value in equation:
3 x + 5 y = 21
3 ∙ ( 8 - 2 y ) + 5 y = 21
24 - 6 y + 5 y = 21
24 - y = 21
Subtract 24 to both sides
- y = - 3
Multiply both sides by - 1
y = 3
x = 8 - 2 y
x = 8 - 2 ∙ 3
x = 8 - 6
x = 2
You can write solution as ( 2 , 3 )