I'll just do the second one, the only one with a fraction solution: { x + 3y = 11 {4x - 3y = -2 To eliminate the x's multiply the first equation through by -4, so that its first term will become -4x and will cancel with the 4x in the second equation: -4x - 12y = -44 4x - 3y = -2 Now when we add them term by term vertically we get: -4x - 12y = -44 4x - 3y = -2 --------------- -15y = -46 y =y = Now to eliminate the y's, we don't need to multiply either one through because the terms in y are already opposite and will cancel just as they are. So we add term by term vertically: { x + 3y = 11 {4x - 3y = -2 ------------- 5x = 9 x = Solution is (x,y) = Here are the solutions to the others. You can solve them similar to the way I solved the second one: {-x+3y=-1 {x-2y=2 BY elmination: Solution is (x,y) = (4,1) {x+y=7 {x+3y=11 by elmination: Solved above. {4x-3y=-2 {4x+5y=14 by elmination: Solution is (x,y) = (1,2) {x+2y=10 {3x-y=9 By elmination Solution is (x,y) = (4,3) Edwin