Solve the following simultaneous equations: 2x - y = 7 and x^2 + y^2 = 34

First, clearly write the two equations above one another, and label them (1) and (2). Rearrange the linear equation (the one with no squared variables) to make y the subject of the equation. You should get y = 2x - 7. Substitute this value of y into the other equation. Remember that you must squared the whole expression of y that you have substituted. You should get x^2 + (2x-7)^2 = 34. Expand all the brackets and group all like terms. By this point you should only have x's left. Since we have some x^2 and some only x, look to form a quadratic equation: 5x^2 - 28x +15 = 0. You can now use the quadratic formula to find x. Use your values of x in one of your original simultaneous equations to find two values of y.