System 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 it mean if a system of equations has no solution?

Back

It means the equations represent parallel lines that never intersect.

Front

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

Back

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

Front

How do you solve a system of equations by substitution?

Back

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

Front

How do you solve a system of equations by graphing?

Back

1. Graph both equations on the same coordinate plane. 2. Identify the point(s) where the lines intersect.

Front

What is the solution to the system: 3x + y = -14 and -2x - y = 9?

Back

(-5, 1)

Front

What is the solution to the system: y = 4x + 1 and 3x + 2y = 13?

Back

(1, 5)

Front

What is the slope of the line represented by the equation 2x + 3y = 6?

Back

The slope is -2/3.

Front

What is the y-intercept of the equation y = 2x + 3?

Back

The y-intercept is 3.

Front

What does it mean for two equations to be consistent?

Back

It means the equations have at least one solution.