Systems of Equations: Substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

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

Back

It means that the equations represent parallel lines that never intersect.

Front

What does it mean when a system of equations has infinite solutions?

Back

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

Front

How do you solve a system of equations using substitution?

Back

You solve one equation for one variable and substitute that expression into the other equation.

Front

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

Back

Isolate one variable in one of the equations.

Front

If you have the equations y = 2x + 3 and y = -x + 1, how do you find the solution?

Back

Set 2x + 3 = -x + 1 and solve for x.

Front

What does the solution (x, y) represent in a system of equations?

Back

It represents the point where the graphs of the equations intersect.

Front

What is the graphical representation of a system of equations with no solution?

Back

Two parallel lines that do not intersect.

Front

What is the graphical representation of a system of equations with infinite solutions?

Back

Two overlapping lines that are the same.

Front

What is the significance of the coefficients in a system of equations?

Back

They determine the slope and position of the lines represented by the equations.