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 an ordered pair to be a solution of a system of equations?

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An ordered pair (x, y) is a solution of a system of equations if it satisfies all equations in the system when substituted for x and y.

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

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Substitute the x and y values of the ordered pair into each equation. If both equations are true, then the ordered pair is a solution.

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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

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 graphical method for solving systems of equations?

Back

The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) where the graphs intersect.

Tags

CCSS.8.EE.C.8B

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What does it mean if two lines are parallel in the context of systems of equations?

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If two lines are parallel, it means they have no points of intersection, indicating that the system of equations has no solution.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if two lines coincide in the context of systems of equations?

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If two lines coincide, they lie on top of each other, indicating that there are infinitely many solutions to the system of equations.

Tags

CCSS.8.EE.C.8A

Front

How do you solve the system of equations: x + 2y = -3 and x - y = -12?

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Using substitution or elimination, the solution is (-9, 3).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the solution to the system of equations: y = 3x - 8 and y = 4 - x?

Back

The solution is the point where the two lines intersect, which is (3, 1).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6