Solve by the linear combination method (with or without multiplication). 2x + 8y = –2 5x + 6y = 9 A. (3, –1) B. (–2, 2) C. (–2, 7) D. (–1, 3)
Do you know substitution (or combination method I guess is what your textbook is calling it)? It's when you isolate a variable in one of the equations. For example, #1: 2x + 8y = -2 If you subtract (8y) from both sides, you end up with: 2x = -8y - 2 Now you divide 2 on both sides to isolate the variable "x" so : x = (-8/2)x - (2/2) or x = -4y - 1 So think... if x = -4y -1, and in the second equation, which is related to the first, 5x + 6y = 9 then can't we simply put what "x" is, which we know is "-4y - 1", into the second equation. We end up with: 5 (-4y - 1) + 6y = 9 Now distribute the 5 first to the "-4y" and the "-1" and you get: -20y - 5 + 6y = 9 Combine like terms: -14y - 5 = 9 Add (5) to both sides: -14y = 14 Divide both sides by (-14) and you get: y = -1 Now all you do is plug in (-1) for "y" in one of the equations (doesn't matter which) and find x. So lets use the first equation: 2x + 8y = -2 Plug in (-1) for y: 2x + 8(-1) = -2 Multiply: 2x + (-8) = -2 Add (8) to both sides: 2x = 6 Finally divide by 2: x = 3 The format for a set of equations is (x,y) so the answer is (3,-1) which is (A) Keep in mind that you could have solved for any variable in the beginning. I just chose "x" because it seemed simpler. Please use this as an example for the rest of your problems. If you need extra explanations, just reply.