Solve Systems of Equations using Substitution

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 it mean for a system of equations to have no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

What does it mean for a system of equations to have infinite solutions?

Back

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

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

How do you solve the system of equations: y = 2x + 3 and y = 4x - 1?

Back

Set 2x + 3 = 4x - 1, solve for x, then substitute back to find y.

Front

What is the solution to the system of equations: y = 3x - 8 and y = 4 - x?

Back

(3, 1)

Front

How do you determine if a system of equations has one solution, no solution, or infinite solutions?

Back

By analyzing the slopes and y-intercepts of the 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.

Front

If x = 6, what is the value of y in the equation y = 2x - 3?

Back

y = 9, so the solution is (6, 9).

Front

What does it mean if two equations are equivalent?

Back

They represent the same line and have the same solution set.