Solving 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 it mean for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

Front

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

Back

It means the equations represent parallel lines that never intersect.

Front

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

Back

It means the equations represent the same line, so there are countless points of intersection.

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. 3. Solve for the remaining variable.

Front

How do you solve a system of equations using elimination?

Back

1. Align the equations. 2. Multiply one or both equations to get opposite coefficients. 3. Add or subtract the equations to eliminate one variable.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane, where intersections represent solutions.

Front

What is the first step in solving the system: 4x - 2y = 7 and x + 2y = 3?

Back

You can use either substitution or elimination; for substitution, solve one equation for y.

Front

Solve the system: 8x + 4y = 12 and y = -2x + 3.

Back

Infinitely many solutions.

Front

Solve for x and y: 2x − 3y = −1 and y = x − 1.

Back

(4, 3) is the solution.