 Quandaries and Queries Daniel Secondary education Student Simultaneous equations 5x + 3y = 22 4x - 7y = -20 I find this near impossible thanks Hi Daniel, What I want to do is to use the two equations you have to produce one equation in one unknown which I can solve. In other words I want to either eliminate the x terms or eliminate the y terms. I am going to eliminate the y terms. In the first equation the coefficient of y is 3 and in the second equation the coefficient of y is -7. Hence if I multiply the first equation by 3 the coefficient of y will be 21, and if I multiply the second equation by 3 the coefficient of y will be -21. If I then add the two equations the y terms will disappear. 5x + 3y = 22 4x - 7y = -20 Multiply the first equation by 7 and the second by 3 7 (5x + 3y) = 7 22 3 (4x - 7y) = -3 20 so 35x + 21y = 154 12x - 21y = -60 Add the two equations to get 47x = 94 and hence x = 2. If you now substitute x = 2 into the first equation you get 5 2 + 3y = 22 3y = 12 y = 4. Penny   