Systems of Equations REVIEW

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 a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

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 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

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

How do you graph a system of equations?

Back

By plotting each equation on the same coordinate plane and identifying points of intersection.

Front

What is the first step in solving the system: 3x - y = 7 and 2x + y = 3?

Back

You can use either substitution or elimination; for substitution, solve one equation for y.

Front

What is the solution to the system: y = 4x + 1 and 3x + 2y = 13?

Back

(1, 5) is the solution.

Front

What does the graph of the equations y = 6x - 11 and -2x - 3y = -7 look like?

Back

The lines intersect at the solution point.