Systems of Linear Equations

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What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect.

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 no solution?

Back

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

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CCSS.8.EE.C.8A

Front

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

Back

It means the lines represented by the equations are the same line, overlapping each other.

Tags

CCSS.8.EE.C.8A

Front

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

Back

Substitute the ordered pair into each equation. If it satisfies both equations, it is a solution.

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

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The graphical representation consists of lines on a coordinate plane, where the intersection point(s) represent the solution(s).

Tags

CCSS.8.EE.C.8A

Front

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

Back

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CCSS.8.EE.B.6

CCSS.8.F.A.3

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

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The slope indicates the steepness of the line and the direction it moves (positive slope goes up, negative slope goes down).

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CCSS.8.EE.B.5

Front

How do you find the solution to a system of equations graphically?

Back

Plot both equations on the same graph 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?

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The substitution method 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

Front

What is the elimination method for solving systems of equations?

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The elimination method 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