Substitution: Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does substitution mean in the context of systems of equations?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted into another equation.

Front

How do you solve for x in the equation 9x = 36?

Back

Divide both sides by 9: x = 36 / 9 = 4.

Front

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

Back

It means that the equations represent the same line, and there are countless points (x, y) that satisfy both equations.

Front

What is the first step in using substitution to solve a system of equations?

Back

Solve one of the equations for one variable in terms of the other variable.

Front

If you have the equation y = -3x + 19, how would you substitute it into the equation 3x - 2y = -2?

Back

Replace y in the second equation: 3x - 2(-3x + 19) = -2.

Front

What does it mean if you get a statement like 5 = 5 when solving a system of equations?

Back

It indicates that the system has infinite solutions.

Front

What is the solution to the equation 2x + 3 = -3x + 3?

Back

x = 0.

Front

What is the correct substitution for the equations x = -2y + 4 and -5x + 4y = 8?

Back

-5(-2y + 4) + 4y = 8.

Front

What is the solution to the equation 3x - 2y = -2 when y = -3x + 19?

Back

Substituting gives 3x - 2(-3x + 19) = -2.