Systems

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 if a system of equations has one solution?

Back

The graphs of the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has no solution?

Back

The graphs of the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The graphs of the equations are the same line (coinciding lines).

Tags

CCSS.8.EE.C.8A

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the equations' graphs.

Tags

CCSS.8.EE.C.8B

Front

What is the graphical representation of intersecting lines?

Back

Two lines that cross at a single point, indicating one solution.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of parallel lines?

Back

Two lines that never meet, indicating no solution.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of coinciding lines?

Back

Two lines that lie on top of each other, indicating infinitely many solutions.

Tags

CCSS.8.EE.C.8A

Front

How do you solve a system of equations using substitution?

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

How do you solve a system of equations using elimination?

Back

Add or subtract equations to eliminate one variable, then solve for the remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6