Unit 4 Review - Systems of Equations

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What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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 a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

Tags

CCSS.8.EE.C.8B

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

Back

It means that the equations represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

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

Back

It means that the equations represent the same line, so any point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you solve a system of equations using elimination?

Back

1. Align the equations. 2. Multiply one or both equations to get opposite coefficients for one variable. 3. Add or subtract the equations to eliminate that variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of the lines of the equations plotted on a coordinate plane.

Tags

CCSS.8.EE.C.8A

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What is the significance of the point of intersection in a system of equations?

Back

The point of intersection represents the solution to the system, where the values of the variables satisfy all equations.

Tags

CCSS.8.EE.C.8B

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What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols like <, >, ≤, or ≥.

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How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid line (for ≤ or ≥) or dashed line (for < or >). 2. Shade the region that satisfies the inequality.

Tags

CCSS.HSA.REI.D.12