Solving equations by elimination
This is a graphical demonstration of the elimination method of solving a system of linear equations. In this case, we start with example 1 from the Solving systems using elimination, day 2 handout, which contains this system:
4x − 3y = 11
3x + 2y = −13
When you press the button below, you should see a blue and a red line, corresponding to the blue and red equations above. There are also blue and red sliders p and q, for the numbers to multiply by the blue equation and the red equation.
When either p or q is nonzero, a green line appears which is the graph of p times the blue equation and q times the red equation. Notice that no matter what p and q are, the green line intersects the blue and red lines where the blue and red lines already intersect, so any point on the green line that is also on either the blue or the red line will be the solution to the system. But when you adjust p and q properly, you'll have a vertical or horizontal line, which will tell you immediately either the x or y of the solution.
For example, when you set p to 4 and q to −3, the x's cancel and you are left with the horizontal line −17y = 85 (which geogebra unfortunately simpilifies to y = −5).