Systems of Equations and Inequalities

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 no solution?

Back

It means the equations represent parallel lines that never intersect.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

Solve by elimination: 3x + 7y = 23 and -3x - 7y = -17

Back

No solution.

Front

Solve the system using elimination: 2x + 3y = 12 and 5x - y = 13

Back

(3, 2).

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

Solve by elimination: 4x - 6y = -6 and -2x - 12y = -12

Back

(0, 1).

Front

What is the graphical representation of a system with one solution?

Back

Two lines that intersect at a single point.

Front

What does the graph of the equations y = 2x + 1 and y = 4x + 1 look like?

Back

They are two lines with different slopes, intersecting at one point.

Front

If a system of equations has no solution, what does the graph look like?

Back

Parallel lines.