Subject: common solution Name: Samantha Who is asking: Student Level: Middle Question: Solve for common solution: x+y=6 2x-3y=2 Solve for y in terms of x: 3x-y=4 Hi Samantha, For the first problem think of (x,y) as a fixed point that is on both graphs, x+y=6 and 2x-3y=2. Since (x,y) is on the first graph the numbers x and y are related by x+y=6. Subtracting x from both sides this relationship becomes y = 6 - x. Since (x,y) is also on the graph of the second equation the numbers x and y satisify the second equation 2x-3y=2. But we know that y = 6 - x and hence 2x - 3(6 - x) = 2 Simplify this expression and solve for x. Once you know x you can find y since y = 6 - x. For the second problem you are looking for an expression that is equivalent to 3x - y = 4 which is of the form y = some expression that doesn't involve y. If you subtract 3x from both sides of the expression 3x - y = 4 you get 3x - y -3x = 4 - 3x or -y = 4 - 3x Multiplying both sides by -1 gives y = 3x - 4 Cheers, Penny Go to Math Central