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 x + 2y = 2 and x = -4y + 2, what is the solution?

Back

(2, 0)

Front

If y = -6x + 5 and -2x + y = 5, what is the solution?

Back

(0, 5)

Front

If y = -2x + 5 and y = 2x - 11, what is the solution?

Back

(4, -3)

Front

What is the substitution method used for?

Back

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

Front

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

Back

It means 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

It means the equations represent the same line, so 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.