Systems of Quadratic and Linear Equations, in Depth - Expii

If you substitute a linear equation, like x=3-y, into a quadratic equation, like x²+y²=5 or x²-y²=5, the resulting equation, like (3-y)²+y²=5 or (3-y)²-y²=5, might be a quadratic or linear equation that you can solve. There might be more than one solution for the remaining variable (in this case y), but you can just plug in all solutions to find the other variables (in this case x=3-y). As always, you can check your final solutions (x,y) by plugging in and seeing if the equations hold true.