With simultaneous equations, we inspect them and look for a way to eliminate one variable. We can do this by substitution. What's the easiest substitution we could make? From the second equation x=(-3-5y)/2. Substitute this in the first equation and we get (5/2)(-3-5y)-6y=48. Multiply through by 2 to get rid of the fraction and we get 5(-3-5y)-12y=96. Opening the brackets: -15-25y-12y=96. That is, -37y-15=96, or 37y=-111, from which y=-3. We can now substitute this value in either equation to get x. 2x+5y=-3 becomes 2x-15=-3, so 2x=12 and x=6.
An alternative solution is to multiply each equation by numbers that will cause a variable to drop out if the revised equations are added or subtracted. If we multiply the first by 2 and the second by 5 we get 10x-12y=96 and 10x+25y=-15. If we subtract the former from the latter we get 37y=-111, so y=-3. Then we can do the substitution as before.
Just check both equations by substituting x=6 and y=-3 to confirm the solution.