Solving Systems of Linear Equations in Two Variables

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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.

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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 every point on the line is a solution.

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CCSS.8.EE.C.8A

Front

How do you solve a system of equations by graphing?

Back

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

Tags

CCSS.8.EE.C.8B

Front

What is the elimination method for solving systems of equations?

Back

A method that involves adding or subtracting 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 substitution method for solving systems of equations?

Back

A method where you 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 slope-intercept form of a linear equation?

Back

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

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CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What is the point of intersection of two lines?

Back

The point where the two lines meet, representing the solution to the system of equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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