Systems of Equations - Substitution

Front

What is a system of equations?

Back

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.

Front

What does it mean to solve a system of equations by substitution?

Back

Solving by substitution involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the first step in solving a system of equations using substitution?

Back

The first step is to isolate one variable in one of the equations.

Front

Back

The solution is (-5, 1).

Front

Back

The solution is (-4, 3).

Front

What does it mean if a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

Back

The solution is (-3, -6).

Front

What does it mean if a system of equations has infinitely many solutions?

Back

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

Front

Back

The solution is (4, 1).

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and intercepts of the lines represented by the equations.