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 if a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and 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

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection points of the lines on a coordinate plane.

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

Back

(−2, −1) is the solution.

Front

What is the solution to the system of equations 2x + 3y = 6 and 4x + 6y = 12?

Back

Infinitely many solutions, as the second equation is a multiple of the first.

Front

What is the solution to the system of equations 3x + 2y = 12 and 3x + 2y = 8?

Back

No solution, as the lines are parallel.

Front

What does it mean for a system of equations to have one solution?

Back

It means the lines intersect at exactly one point.