Systems of Equations - Review

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 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. 3. Solve for the remaining variable.

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. 3. Solve for the remaining variable.

Front

What is the graphical representation of a system of equations?

Back

The solutions are represented by the points where the graphs of the equations intersect.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you determine if two lines are parallel from their equations?

Back

If the slopes (m) of the two lines are equal, the lines are parallel.

Front

What is the solution to the system of equations: 3x + 2y = 16 and 7x + y = 19?

Back

(2, 5)