These are simultaneous equations and we need to find the value of X and Y. We can use the elimination method. The coefficients (the amount the letter is being multiplied by) of X and Y do not match. First, we need to create common coefficients to help us solve the problem. I have chosen to create the value of Ys the same. We can multiply the first equation (3x+5y=19) by 2 and the second equation (4x-2y=-18) by 5. We now have 6x+10y=38 and 20x-10y=-90. Now we can add these two new equations together to eliminate Y. This gives us 26x=-52. We can now find X by dividing both sides by 26. x=-2Now we can sub X into the first equation to find Y. Doing this gives us 3(-2)+5y=19. We now can expand the brackets to give -6+5y=19. Add 6 to both sides to get Y on its own. We now have 5y=25. Divide by 5 to get one lot of Y and we get y=5. We now know x=-2 and y=5. Finally check your answer by putting the values of X and Y in the second equation. 4(-2)-2(5)=-8-10=-18. This is correct.

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