3x + 5y=21, 2x + 3y=13

Answer 1

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

Answer 2

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 )