TEKS A.2I: Writing Systems of Equations

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution to the system is the set of values that satisfy all equations simultaneously.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you represent a word problem as a system of equations?

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Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

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CCSS.HSA.CED.A.3

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What does it mean for two equations to be consistent?

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Two equations are consistent if they have at least one solution in common.

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CCSS.8.EE.C.8B

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What does it mean for two equations to be independent?

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Two equations are independent if they represent different lines that intersect at exactly one point.

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CCSS.8.EE.C.8A

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What does it mean for two equations to be dependent?

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Two equations are dependent if they represent the same line, meaning they have infinitely many solutions.

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CCSS.8.EE.C.8B

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How can you solve a system of equations graphically?

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To solve graphically, plot both equations on the same graph and identify the point(s) where they intersect.

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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.

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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

Front

What is the significance of the coefficients in a system of equations?

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Coefficients represent the relationship between the variables in the equations; they determine the slope and position of the lines when graphed.

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CCSS.8.EE.C.8A

Front

How do you check the solution of a system of equations?

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Substitute the solution back into the original equations to verify that both equations are satisfied.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6