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 for a system of equations to have one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations coincide, meaning they are the same line.

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

How do you solve a system of equations using elimination?

Back

Add or subtract the equations to eliminate one variable, then solve for the remaining variable.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines or curves on a coordinate plane.

Front

What is the solution to the system: 2x - 3y = 6 and 7x - 3y = -9?

Back

(-3, -4)

Front

What is the solution to the system: x + 9y = 8 and -6x - 9y = -3?

Back

(-1, 1)

Front

What is the solution to the system: 5x - 4y = -16 and x + 2y = -6?

Back

(-4, -1)