Systems of Linear Equations

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

Tags

CCSS.8.EE.C.8B

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.

Tags

CCSS.8.EE.C.8A

Front

What does it mean for a system of equations to have infinite solutions?

Back

It means that 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 linear equations by graphing?

Back

Graph each equation on the same coordinate plane and identify the point(s) where the lines intersect.

Tags

CCSS.8.EE.C.8B

Front

What is the substitution method for solving systems of equations?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method for solving systems of equations?

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 the solution to the system x - y = 11 and 2x + y = 19?

Back

The solution is the point (10, -1) where the two lines intersect.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to the system 2x - y = 0 and 4x - y = 0?

Back

The solution is (0, 0), indicating infinite solutions since both equations represent the same line.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to the system of equations represented by the lines y = 2x + 1 and y = -x + 5?

Back

The solution is the point where the two lines intersect, which can be found by solving the equations simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6