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.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 lines represented by the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

What does it mean for a system of equations to have no solution?

Back

It means that the lines represented by the equations are parallel and never intersect.

Tags

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 lines represented by the equations coincide, or are the same line.

Tags

CCSS.8.EE.C.8A

Front

How do you determine if an ordered pair is a solution to a system of equations?

Back

Substitute the values of the ordered pair into both equations and check if both equations are true.

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What is the graphical representation of a system of linear equations?

Back

The graphical representation consists of lines on a coordinate plane.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How can you find the intersection point of two lines algebraically?

Back

By solving the system of equations simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients determine the slope and position of the line on the graph.

Front

What is the method of substitution in solving systems of equations?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6