Solve the simultaneous equations: 3x+5y=19, 4x-2y=-18

For all simultaneous equations it is useful to number each one to keep your working clear and concise. In order to solve this we need to eliminate one of the variables (x or y) by manipulating the equations. I would multiply the first equation by 2 and the second equation by 5. This gives you a third equation; 6x+10y=38 and a fourth; 20x-10y=-90.Now we are able to solve the equation through elimination. As we have 10y in one equation and -10y in the other, we can add the two equations together so that the y variable cancels out. Doing this gives: 26x=-52. We can then divide by 26 to give the first solution: x=-2. Then we can substitute this answer in to one of the original equations and solve for y. The final answer is y=5 and x=-2.