Solve Systems of Equations by Substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the substitution method?

Back

A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

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

Back

Get either variable by itself.

Front

If two lines intersect at one point, how many solutions does the system have?

Back

One solution.

Front

If two lines are parallel, what can be said about the solutions of the system?

Back

No solution.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

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

Front

Solve the system: y = 2x + 1 and y = 4x - 1. What is the solution?

Back

(1, 3)

Front

Solve the system: y = -2x + 5 and y = 2x - 11. What is the solution?

Back

(4, -3)