Solutions to Systems of Equations Practice - A

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 unique solution?

Back

It means the lines intersect at exactly one point.

Front

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

Back

It means the lines are parallel and never intersect.

Front

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

Back

It means the lines coincide, or are the same line.

Front

How do you determine if an ordered pair is a solution to a system of equations?

Back

Substitute the ordered pair into each equation; if both equations are true, it is a solution.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

What is the graphical method for solving systems of equations?

Back

A method where each equation is graphed on the same coordinate plane, and the point(s) of intersection are the solutions.

Front

If the equations are x - y = 6 and x = 11, what is the solution?

Back

(11, 5)

Front

If the equations are y = 4x + 1 and 3x + 2y = 13, what is the solution?

Back

(1, 5)