Solving Systems Using Substitution

Front

What is a solution to a system of equations that results in no x or y value that will satisfy both equations?

Back

No Solution

Front

What is a solution to a system that results in an unlimited amount of x values and an unlimited amount of y values that will satisfy both equations?

Back

Infinite Solutions

Front

Solve the following systems of equations using substitution: x = 6, y = 2x - 3

Back

(6, 9)

Front

Solve the system of equations: 2x + 3y = 4, y = 5x - 27

Back

(5, -2)

Front

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

Back

It means that the equations represent the same line, and there are unlimited points (x, y) that satisfy both equations.

Front

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

Back

Solve one of the equations for one variable in terms of the other variable.

Front

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

Back

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

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations overlap completely.

Front

How do you check if your solution to a system of equations is correct?

Back

Substitute the solution back into both original equations to see if they hold true.