EE7 (Number of Solutions of Linear Equations)

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What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form ax + b = c, where a, b, and c are constants.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What does it mean for a linear equation to have one solution?

Back

A linear equation has one solution when the graph of the equation intersects the x-axis at exactly one point.

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CCSS.HSF-IF.C.7A

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What does it mean for a linear equation to have infinitely many solutions?

Back

A linear equation has infinitely many solutions when the two sides of the equation are equivalent for all values of x, resulting in the same line on a graph.

Tags

CCSS.8.EE.B.5

Front

What does it mean for a linear equation to have no solution?

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A linear equation has no solution when the lines represented by the equations are parallel and never intersect.

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CCSS.8.EE.C.8A

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How do you determine the number of solutions for a system of linear equations?

Back

You can determine the number of solutions by graphing the equations and observing their intersection points: one solution (intersecting), infinitely many solutions (same line), or no solution (parallel lines).

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CCSS.8.EE.C.8B

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What is the sales tax rate in Langston's guitar purchase problem?

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The sales tax rate is 7%.

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CCSS.8.EE.C.7B

Front

If Langston has $62 and needs $200 plus sales tax, how much more money does he need?

Back

Langston needs $200 + (7% of $200) = $200 + $14 = $214. He has $62, so he needs $214 - $62 = $152 more.

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CCSS.6.EE.B.7

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How much does Langston save from his weekly earnings?

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Langston saves half of his weekly earnings of $22, which is $11.

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CCSS.6.EE.B.6

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How many weeks will it take Langston to save enough for the guitar?

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Langston needs $152 more and saves $11 per week. It will take 152 / 11 = approximately 13.82 weeks, which rounds up to 14 weeks.

Tags

CCSS.6.EE.B.7

Front

What is the solution for x in the equation 5(x−4)=2+3x?

Back

The solution for x is 11.

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CCSS.8.EE.C.7B