Systems of Equations - word problems

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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 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

Front

What does it mean to graph a system of equations?

Back

Graphing a system of equations involves plotting each equation on the same coordinate plane to find the point(s) of intersection, which represent the solution(s).

Tags

CCSS.8.EE.C.8B

Front

What is the elimination method for 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 variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is a consistent system of equations?

Back

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

Tags

CCSS.8.EE.C.8A

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

Front

What is a dependent system of equations?

Back

A dependent system has infinitely many solutions, meaning the equations represent the same line.

Tags

CCSS.8.EE.C.8B

Front

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

Back

Identify the variables, translate the relationships and conditions into equations, and then form a system of equations.

Tags

CCSS.HSA.CED.A.3

Front

What is the first step in solving a word problem involving a system of equations?

Back

Read the problem carefully, identify the variables, and determine the relationships between them.

Tags

CCSS.8.EE.C.8C

Front

Example of a word problem: The sum of two numbers is 10. What are the equations?

Back

x + y = 10.

Tags

CCSS.HSA.CED.A.3