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 a 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

What is the substitution method?

Back

A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

Front

What is graphing in the context of systems of equations?

Back

A method of solving systems by plotting the equations on a graph and identifying the point(s) of intersection.

Front

What is the y-coordinate of the solution to the system: x - 2y = 1 and x + 4y = 7?

Back

1

Front

Which of the following is not a method for solving systems of equations: Elimination, Substitution, Estimation, Graphing?

Back

Estimation

Front

What is the solution to the system: 2x + 3y = 6 and x - y = 1?

Back

(3, 0)