Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

The lines represented by the equations are parallel, having the same slope but different y-intercepts.

Tags

CCSS.8.EE.C.8A

Front

What is the solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Tags

CCSS.8.EE.C.8B

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

How can you determine if two equations are equivalent?

Back

If one equation can be transformed into the other by multiplying or dividing by a non-zero number.

Tags

CCSS.8.EE.C.7A

Front

What is the slope of a line in the context of a linear equation?

Back

The slope indicates the steepness of the line and is calculated as the change in y over the change in x (rise/run).

Tags

CCSS.8.EE.B.5

Front

What is a y-intercept?

Back

The point where a line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How do you graph a system of equations?

Back

Graph each equation on the same coordinate plane and identify the point(s) of intersection.

Tags

CCSS.8.EE.C.8B