Solving 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 a unique solution?

Back

It means that the equations intersect at exactly one point on a graph.

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CCSS.8.EE.C.8A

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.

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CCSS.8.EE.C.8A

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, or coinciding lines.

Tags

CCSS.8.EE.C.8A

Front

How do you solve a system of equations using substitution?

Back

Replace one variable with an expression from another equation and solve for the remaining variable.

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, making it easier to solve for the other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of intersecting lines?

Back

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

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of parallel lines?

Back

Two lines that run alongside each other without ever meeting, 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

Solve for x and y: 5x + 3y = 7, y = 4

Back

(-1, 4)