Solve 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 of equations by substitution?

Back

Isolate one variable in one of the equations.

Front

If two lines are parallel, what can be said about their system of equations?

Back

The system has 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 solution back into both original equations to see if they hold true.

Front

What is the substitution method used for?

Back

To find the values of variables that satisfy all equations in a system.

Front

Solve the system by substitution: y = 2x - 11, -3y = -6x - 15

Back

No solution (parallel lines).

Front

Solve the system by substitution: x + 2y = 2, x = -4y + 2

Back

(2, 0).

Front

Solve the system by substitution: 5x + 4y = -14, y = -7x - 15

Back

(-2, -1).