Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for a system of equations to have one solution?

Back

The graphs of the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The graphs of the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The graphs of the equations coincide, meaning they are the same line.

Tags

CCSS.8.EE.C.8A

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if both equations are true, it is a solution.

Front

What is the substitution method in solving systems of equations?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method in solving systems of equations?

Back

Add or subtract equations to eliminate one variable, making it easier to solve for the other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to graph a system of equations?

Back

Plotting each equation on the same coordinate plane to find points of intersection.

Tags

CCSS.8.EE.C.8B

Front

What is the significance of the coefficients in a system of equations?

Back

They determine the slope and position of the lines represented by the equations.

Tags

CCSS.8.EE.C.8A

Front

What is a consistent system of equations?

Back

A system that has at least one solution.

Tags

CCSS.8.EE.C.8B