Solving systems of equations 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?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is substitution in solving equations?

Back

Replacing one variable with an expression derived from another equation.

Front

How do you use substitution to solve a system of equations?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation.

Front

What is the solution to the system of equations y = 2x + 1 and y = 4x - 1?

Back

(1, 3)

Front

What is the solution to the system of equations y = -5x and x + 3y = 28?

Back

(-2, 10)

Front

What is the solution to the system of equations y = -2x + 5 and y = 2x - 11?

Back

(4, -3)

Front

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

Back

The lines represented by the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, so every point on the line is a solution.

Front

What is the first step in solving the system of equations y = 3x + 2 and y = -x + 4?

Back

Set the two equations equal to each other: 3x + 2 = -x + 4.