Solving Systems by Graphing, Substitution & Elimination

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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 is the point(s) where the equations intersect.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean to solve a system of equations by graphing?

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Solving by graphing involves plotting each equation on the same coordinate plane and identifying the point(s) where they intersect.

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CCSS.8.EE.C.8B

Front

What is the elimination method in 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 variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method in solving systems of equations?

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The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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How do you determine if a system of equations has no solution?

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A system has no solution if the lines represented by the equations are parallel, meaning they never intersect.

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CCSS.8.EE.C.8A

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How do you determine if a system of equations has infinitely many solutions?

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A system has infinitely many solutions if the equations represent the same line, meaning they overlap completely.

Tags

CCSS.8.EE.C.8A

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Multiply the first equation by 3 and the second equation by 4 to align the coefficients of x.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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Back

Multiply the equation by -4.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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The solution is (-4, -2).

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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The solution is (-6, 7).

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6