To solve this system of equations, we can use the method of substitution or elimination.

Method of substitution:

Solve the first equation for y: y = x - 6Substitute this expression for y into the second equation: 5x - 2(x - 6) = -3Simplify and solve for x: 5x - 2x + 12 = -3
3x = -15
x = -5Substitute x = -5 back into the first equation to find y: y = -5 - 6
y = -11

Therefore, the solution to the system of equations is x = -5 and y = -11.