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 by substitution?

Back

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

Front

How do you isolate a variable in an equation?

Back

By performing inverse operations to get the variable alone on one side of the equation.

Front

What is the first step in solving the system: x + 2y = 2 and x = -4y + 2?

Back

Substitute -4y + 2 for x in the first equation.

Front

What is the solution to the system: x + 2y = 2 and x = -4y + 2?

Back

(2, 0)

Front

What is the substitution method used for?

Back

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

Front

What does it mean if two equations have no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What does it mean if two equations have infinitely many solutions?

Back

It means the equations represent the same line, and every point on the line is a solution.

Front

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

Back

By substituting the solution back into the original equations to see if they hold true.

Front

What is the solution to the system: 5x + 4y = -14 and y = -7x - 15?

Back

(-2, -1)