Systems 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 set of values that satisfy all equations in the system.

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 ensure the equations reflect the problem's constraints.

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CCSS.HSA.CED.A.3

Front

What does it mean to solve a system of equations?

Back

To find the values of the variables that make all equations in the system true.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then 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 remaining 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 they satisfy all equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is a word problem involving animals and legs?

Back

A common type of problem where you determine the number of different animals based on the total number of legs they have.

Tags

CCSS.8.EE.C.8C

Front

If a pig has 4 legs and a duck has 2 legs, how do you set up an equation for a problem involving these animals?

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Let x be the number of pigs and y be the number of ducks. The equation would be 4x + 2y = total legs.

Front

What is a common strategy for solving age-related word problems?

Back

Define variables for the ages, translate the relationships into equations, and solve the system of equations.

Tags

CCSS.8.EE.C.8C

Front

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

Back

It means that the equations represent parallel lines that never intersect, indicating that there are no values that satisfy all equations.

Tags

CCSS.8.EE.C.8A