Solve the simultaneous equations: 2x-3y = 24 and 6x+2y = -5

There are numerous alternative ways to solve these simultaneous equations. For this problem, one of the simplest methods is to multiply the first equation by 3, so that we get 6x in both equations:

(2x - 3y)3 = 243, giving 6x - 9y = 72

If we now subtract the second equation from the first one (multiplied by 3), we get:

(6x - 9y) - (6x + 2y) = 72-(-5)

This way we are left only with y on the left hand side:

-9y - 2y = 77

-11y = 77

Thus we found the value of y:

y = -77/11 = -7

Now we can substitute the value for y into the first equation and find x (substituting into the 2nd equation would also work fine):

2x - 3(-7) = 24

2x + 21 = 24

2x = 3

x = 3/2

Therefore, the solution is: x = 3/2 and y= -7