Writing 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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How do you solve a system of equations using substitution?

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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

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What does it mean if a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has infinitely many solutions?

Back

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

Tags

CCSS.8.EE.C.8A

Front

How can you represent a word problem as a system of equations?

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Identify the variables, translate the relationships into equations, and ensure the equations reflect the problem's constraints.

Tags

CCSS.HSA.CED.A.3

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What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines (or curves) on a coordinate plane, where the intersection points represent the solutions.

Tags

CCSS.8.EE.C.8B

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

Identify the unknowns, create equations based on the relationships described, and ensure they reflect the total quantities involved.

Tags

CCSS.8.EE.C.8C

Front

What is the slope-intercept form of a linear equation?

Back

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How do you find the y-intercept of a linear equation?

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