This is how you do an elimination question. I will show my work again at the end after I explain each step. 5x - 2y = 4 2x + 3y = 13 You can choose to either work with 5x and 2x or -2y and 3y. I am going to eliminate x. Step 1 What is the lowest common factor of 5 and 2. In other words what number can both 5 and 2 go into evenly. The answer is 10. Now you want to make the coefficients of x, (the number in front of x) opposites. Which means you are going to multiply one equation by a positive number and the other by a negative one. So again the original two equations are: 5x - 2y = 4 2x + 3y = 13 The common factor of 5 and 2 was 10. So I multiply the entire 1st equation by (2) since 2 times 5 is 10. I multiply the entire 2nd equation by (-5) because I want one of the coeffiecients of x to be negative and one positive. (2)*5x -(2)*2y = (2)*4 (* means multiply) = 10x - 4y = 8 (-5)*2x + (-5)*3y = (-5)*13 So the two equations now look like this: 10x - 4y = 8 -10x - 15y = -65 Now add the two equations together. 10x - 4y = 8 + -10x - 15y = -65 ___________________ -19y = -57 Solve for y y = 3 Now to find x go to one of the ORIGINAL equations and replace y with 3. 2x + 3(3) = 13 2x + 9 = 13 Solve for x x = 2 X Y Your solution set is (2,3) You can check your answer by making sure both numbers plug into the original equations. Now here it is again with out all of the explanation in the middle. 5x - 2y = 4 2x + 3y = 13 (2)5x - (2)2y = 2(4) (-5)2x + (-5)3y = (-5)13 10x - 4y = 8 + -10x - 15y = -65 ________________ -19y = -57 -57 ___ = 3 y = 3 -19 2x + 3(3) = 13 2x + 9 = 13 2x = 4 x = 2 Check 5(2) - 2(3) = 4 10 - 6 = 4 2(2) + 3(3) = 13 4 + 9 = 13 It is very hard to explain math over the internet but I hope you basically understand what I did.