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

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CCSS.8.EE.C.8B

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.

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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 the equations represent the same line, so there are countless points of intersection.

Tags

CCSS.8.EE.C.8A

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable, then 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 the 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 a system of equations?

Back

The solution is represented by the point(s) where the lines intersect on a graph.

Tags

CCSS.8.EE.C.8A

Front

What is the y-intercept of a linear equation?

Back

The y-coordinate where the line crosses the y-axis (x=0).

Front

What is the slope of a line?

Back

The ratio of the rise (change in y) to the run (change in x) between two points on the line.

Tags

CCSS.8.EE.B.5

Front

How can you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.

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CCSS.8.EE.B.6