Solving Algebraically Algebraic Solutions Use one of three algebraic methods to find the solution without graphing: Substitution Comparison Elimination Which method you choose will depend on the form of the equations, as some methods will be quicker. However, all three methods will work for any system of linear equations. Here is the principle we're going to use. If two lines, when graphed, have an intersection point, then that solution point is on both lines. Think of it as the point where the two lines mix. If we combine the equations of the lines and simplify, the result will be the mixing point, the one point that's on both lines, which will be the solution. Each of the algebraic methods below mix the two equations in different ways. Substitution | Comparison | Elimination Introduction | Solving Graphically | Solving Algebraically | Mixed Practice Resources Content, HTML, graphics & design by Bill Willis 2024