Solving 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 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 for a system of equations to have one solution?

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A system has one solution when the graphs of the equations intersect at exactly one point.

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CCSS.8.EE.C.8A

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What does it mean for a system of equations to have no solution?

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A system has no solution when the equations represent parallel lines that never intersect.

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CCSS.8.EE.C.8A

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What does it mean for a system of equations to have infinitely many solutions?

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A system has infinitely many solutions when the equations represent the same line, meaning they intersect at every point on that line.

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CCSS.8.EE.C.8B

Front

How can you determine the solution of a system of equations graphically?

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You can determine the solution by graphing the equations and identifying the point(s) where the lines intersect.

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CCSS.8.EE.C.8B

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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 then 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 variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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How do you write a system of equations from a word problem?

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Identify the variables, translate the relationships and conditions into equations, and write them as a system.

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CCSS.8.EE.C.8C

Front

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

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Coefficients represent the rate of change of the variables and affect the slope of the lines in the graph.

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CCSS.8.EE.C.8B

Front

What is the graphical representation of the equation y = mx + b?

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This equation represents a straight line where 'm' is the slope and 'b' is the y-intercept.

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CCSS.8.EE.B.6

CCSS.8.F.A.3