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 one solution?

Back

It means that the equations intersect at exactly one point on the graph.

Front

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

Back

It means that 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 that 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. 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

It is the intersection points of the lines represented by the equations on a coordinate plane.

Front

What is the x-coordinate of the solution to the system: 2x + 3y = 15 and -x + 3y = 3?

Back

4

Front

What is the y-coordinate of the solution to the system: 6x + 10y = -32 and 6x + 9y = -27?

Back

y = -5

Front

What is the solution to the system of equations: 2x + 3y = 15 and -x + 3y = 3?

Back

(4, 1)