Solve linear equation by elimination

5x+2y = - 3

3x+3y = 9

Multiply equation 1 by 3 and equation 2 by 5

15x+6y=-9

15x+15y=45

15x+6y - (15x+15y) = -9-45

15x+6y-15x-15y=-54

-9y=-54

y=-54/-9

y=6

Substitute y=6 in equation 2

15x+15 (6) = 45

15x+90=45

15x=45-90

15x=-45

X=-45/15

x = - 3

Therefore, x = - 3, y=6