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 that are solved together.

Front

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

Back

It means to solve one equation for one variable and then substitute that expression into the other equation.

Front

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

Back

Isolate one variable in one of the equations.

Front

Given the equations x = -3y - 17 and 2x + 3y = -7, what is the solution?

Back

(10, -9)

Front

What is the solution to the system of equations 3x + 2y = 8 and -x + y = -11?

Back

(6, -5)

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 the graphical representation of a system of equations?

Back

The point(s) where the lines representing the equations intersect.

Front

What does it mean if two equations have no solution?

Back

The lines are parallel and will never intersect.

Front

What does it mean if two equations have infinite solutions?

Back

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

Front

Given the equations y = 3x - 8 and y = 4 - x, what is the solution?

Back

(3, 1)