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

Front

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

Back

Identify the variables, translate the relationships and conditions into equations, and set them equal to each other based on the problem's context.

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CCSS.HSA.CED.A.3

Front

What does it mean for two equations to have one solution?

Back

It means that the lines represented by the equations intersect at exactly one point, indicating a unique solution for the variables.

Tags

CCSS.8.EE.C.8A

Front

What does it mean for two equations to have no solution?

Back

It means that the lines represented by the equations are parallel and never intersect, indicating that there is no set of values that satisfies both equations.

Tags

CCSS.8.EE.C.8A

Front

What does it mean for two equations to have infinitely many solutions?

Back

It means that the lines represented by the equations coincide, or are the same line, indicating that there are an infinite number of points that satisfy both equations.

Tags

CCSS.8.EE.C.8A

Front

How do you find the cost of items in a word problem involving equations?

Back

Set up equations based on the total cost and the number of items sold, then solve the system of equations to find the individual costs.

Tags

CCSS.8.EE.C.8C

Front

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

Back

The first step is to write the equations in a standard form, if necessary, and then decide on a method to solve them (substitution, elimination, or graphing).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is substitution in solving systems of equations?

Back

Substitution is a method where you solve one equation for one variable and then substitute that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is elimination in solving systems of equations?

Back

Elimination is a method where you add or subtract 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

How can you check the solution of a system of equations?

Back

Substitute the values of the variables back into the original equations to verify that both equations are satisfied.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6