Systems of Equations: Substitution

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Substitution is a method of solving a system of equations by solving one equation for one variable and then substituting that expression into the other equation.

To solve for y, simply substitute any value of x into the equation. For example, if x = 1, then y = 3 - 1 = 2.

The solution is (2, 1).

The solution is (4, 3).

Substitute x = 6 into the equation: y = 2(6) - 3 = 12 - 3 = 9. So, y = 9.

The solution is (6, 9).

It means that the graphs of the equations intersect at exactly one point.

It means that the graphs of the equations are parallel and never intersect.

It means that the equations represent the same line, and every point on the line is a solution.