Solve the following simultaneous equations: 3x - y = 1, 2x + 2y = 2

When we are asked to solve simultaneous equations, what we are being asked to do is find the point where two lines cross. In this case, where we are given two straight lines, there will only be one point where the two lines meet. So we need to find an x and y that are the same for both of the equations. We can do this by eliminating a variable. Let's choose to eliminate y. As we can see the first equation as a '-y' and the second has a '+2y' term. if we multiply the first equation by 2, we can get a '-2y' term. We are left with 2 equations '6x - 2y = 2' and '2x + 2y = 2'. but adding the two rows together we will eliminate the y variable (as -2y is the negative of 2y) and we will get 8x = 4. By dividing both sides by get we see that x = 1/2. We can subsitute this value for x into either one of the equations. Lets choose the second. we get 1 + 2y = 2, which we can rearrane to give us y = 1/2. x=1/2, y=1/2