Solving Systems 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 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 a system by substitution?

Back

Make sure at least one equation is solved for one variable.

Front

If you have the equations x = 2y + 3 and 4x - y = 11, how do you start solving by substitution?

Back

Substitute 2y + 3 for x in the second equation.

Front

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

Back

(-5, -1)

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 solution to the system of equations x = 3y - 13 and 4x + 2y = 4?

Back

(-1, 4)

Front

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

Back

The lines represented by the equations are parallel and never intersect.

Front

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

Back

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

Front

Solve the system: x = -3y - 17 and 2x + 3y = -7.

Back

(10, -9)