Algebra - Unit 5 Review - Systems of Equations

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What is a system of equations?

Back

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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How do you determine if a point is a solution to a system of equations?

Back

Substitute the coordinates of the point into each equation. If the point satisfies all equations, it is a solution.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines represented by the equations.

Tags

CCSS.8.EE.C.8B

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, meaning the lines intersect at one or more points.

Tags

CCSS.8.EE.C.8B

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions, meaning the lines are parallel and never intersect.

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CCSS.8.EE.C.8B

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and 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?

Back

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

How can you represent a system of inequalities graphically?

Back

Graph each inequality on the same coordinate plane, shading the region that satisfies each inequality.

Tags

CCSS.HSA.REI.D.12

Front

What is the significance of the solution to a system of inequalities?

Back

The solution represents all the points that satisfy all inequalities in the system, often forming a shaded region on a graph.

Tags

CCSS.HSA.REI.D.12

Front

What is a linear equation?

Back

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2