Systems of Equations

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What is a system of equations?

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean if a system of linear equations has one solution?

Back

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

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CCSS.8.EE.C.8A

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

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The lines represented by the equations are parallel and never intersect.

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CCSS.8.EE.C.8A

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

Back

The lines represented by the equations coincide, meaning they are the same line.

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CCSS.8.EE.C.8A

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How can you determine if two lines are parallel from their equations?

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If the slopes of the lines are equal and the y-intercepts are different, the lines are parallel.

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CCSS.8.EE.B.5

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What is the substitution method for solving systems of equations?

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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

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What is the elimination method for solving systems of equations?

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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

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What is the graphical method for solving systems of equations?

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A method where each equation is graphed on the same coordinate plane, and the solution is the point of intersection.

Tags

CCSS.8.EE.C.8B

Front

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

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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

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How do you convert a linear equation from standard form to slope-intercept form?

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Rearrange the equation to solve for y in terms of x.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3