Systems of Equations

Front

What is a system of equations?

Back

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

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

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

Front

How do you solve a system of equations using 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 using elimination?

Back

1. Align the equations. 2. Add or subtract the equations to eliminate one variable.

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines represent the solutions to the system.

Front

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

Back

(1, 3)

Front

What is the solution to the system of equations: 2x + 3y = 6 and x - y = 1?

Back

(3, 0)

Front

What is the slope of the line represented by the equation 3x + 4y = 12?

Back

-3/4 (after rearranging to slope-intercept form y = mx + b).

Front

What is the y-intercept of the equation y = 5x - 2?

Back

-2 (the point where the line crosses the y-axis).