Substitution method

Front

What is the substitution method in solving systems of equations?

Back

The substitution method is a technique used to solve systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

What is the first step in the substitution method?

Back

Get either variable by itself in one equation.

Front

Solve the system using substitution: x + 6y = 17, x - 3y = 8.

Back

(11, 1)

Front

Solve the system using substitution: -4x + 4y = 8, y = -2x - 10.

Back

(-4, -2)

Front

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

Back

It means that the lines represented by the equations are parallel and do not intersect.

Front

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

Back

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

Front

Solve: x = -3y - 17, 2x + 3y = -7.

Back

(10, -9)

Front

What is the purpose of the substitution method?

Back

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

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.

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.