Solving 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 substitution in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

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

Back

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

Front

What is an infinite solution in a system of equations?

Back

When the equations represent the same line, resulting in countless solutions.

Front

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

Back

The equations represent parallel lines that never intersect.

Front

Solve the system: 3x + 2y = 8 and -x + y = -11.

Back

(6, -5)

Front

Solve the system: y = 8x + 1 and y = 6x + 3.

Back

(1, 9)

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, what do you do next?

Back

Set the two expressions for y equal to each other: 2x + 3 = -x + 1.