Systems of linear equations

Front

What is a system of linear equations?

Back

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

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What does it mean if two lines on a graph are parallel?

Back

They have no solutions because they never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if two lines on a graph intersect at one point?

Back

There is one unique solution to the system of equations.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if two lines on a graph are the same line?

Back

There are infinite solutions because every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The (x,y) coordinates must satisfy both equations.

Front

What is the substitution method in solving systems of equations?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What is the elimination method in solving systems of equations?

Back

It involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What is the graphical method for solving systems of equations?

Back

It involves graphing both equations on the same coordinate plane and identifying the point(s) of intersection.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to the system of equations y = 2x + 3 and y = -x + 1?

Back

(1, 5) is the solution.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What is the slope-intercept form of a linear equation?

Back

It is written as y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6