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 solve a system of equations using substitution?

Back

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 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 variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Define a linear equation.

Back

A linear equation is an equation that makes a straight line when graphed. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does it mean for a system of equations to be consistent?

Back

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

Tags

CCSS.8.EE.C.8B

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions, meaning the graphs of the equations do not intersect at any point.

Tags

CCSS.8.EE.C.8B

Front

What is the graphical method for solving systems of equations?

Back

The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) where they intersect.

Tags

CCSS.8.EE.C.8B

Front

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

Back

To check the solution, substitute the values of the variables 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 a word problem in the context of systems of equations?

Back

A word problem is a mathematical problem that describes a situation in words, requiring the formulation of equations to find a solution.

Tags

CCSS.8.EE.C.8C

Front

How do you translate a word problem into a system of equations?

Back

Identify the variables, write equations based on the relationships described in the problem, and ensure they represent the situation accurately.

Tags

CCSS.HSA.CED.A.3