Question

What are three different methods for solving systems of equations and when would you use each one?

Answer 1

The first method is substitution. This is when the x or y value that is known is substituted into one of the equations. This should be done when you can easily see or find the x or y value.

Example: x = 3, and x + 8y = 30.

The x was given in the first equation (x = 3), and can therefore be substituted into the other equation to find y.

The next method is elimination. This is when you add the two systems together and eliminate either the x values or the y values. This should be done when there are opposite signs of the same number in both equations.

Example: y - 3x = 24, and 2y + 3x = 7

In the first equation you have -3x, and in the second you have 3x. If you were to add the two equations, the x values would cancel out and you would be left with:

y + 2y = 24 + 7

And then you could solve for y.

The last method is to graph both equations and to see at which point the lines intersect.