3F Systems of Equations - Word Problems 1 5Q

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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 solve a system of equations using substitution?

Back

To solve by substitution, solve one equation for one variable, then substitute that expression into the other equation.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to find the intersection of two lines in a graph?

Back

Finding the intersection of two lines means determining the point where the two lines cross, which represents the solution to the system of equations.

Tags

CCSS.8.EE.C.8B

Front

What is the difference between a linear equation and a nonlinear equation?

Back

A linear equation graphs as a straight line and has no exponents greater than one, while a nonlinear equation can graph as a curve.

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CCSS.8.F.A.3

Front

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

Back

The first step is to define the variables that represent the unknown quantities in the problem.

Tags

CCSS.8.EE.C.8C

Front

How can you check if your solution to a system of equations is correct?

Back

You can check the solution by substituting the values back into the original equations to see if they hold true.

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 other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

A system has no solution if the equations represent parallel lines that never intersect.

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CCSS.8.EE.C.8A

Front

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

Back

A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

How do you set up equations from a word problem?

Back

Identify the relationships described in the problem, define variables, and translate the relationships into mathematical equations.

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CCSS.HSA.CED.A.3