Solve the simultaneous equations 2x - 3y = 24 (1) ; 6x + 2y = -5 (2)

The objective of this question is to solve for x and y. Since we cannot directly eliminate x or y, find the lowest common multiple for x in both equations by comparing 2x in equation 1 with 6x in equation 2. In this case it is 6 and x can be eliminated by multiplying equation 1 by 3. This gives 6x-9y=72. Now subtract equation 2 from the new equation 1 which you just worked out. Working from left to right, you will have 6x -6x=0; -9y-2y= -11y; and 72-(-5) = 72+5=77. Make sure you watch out for the negative signs. The resulting equation is -11y =77. Divide both sides of the equation by -11 to obtain y= 77/-11= -7. Label the equation y=-7 as (3) and substitute equation 3 into equation 1 as follows: 2x-3*(-7)= 24 --> 2x - (-21) = 24 -->2x + 21=24. Subtract 21 from both sides of the equation to obtain 2x = 24-21 --> 2x=3 and x=3/2. We have now solved the equation for x (x=3/2) and y( y=-7).