System of Equations Word Problems

Front

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.HSA.REI.C.6

CCSS.8.EE.C.8B

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.HSA.REI.C.6

CCSS.8.EE.C.8B

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.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

Define a linear equation.

Back

A linear equation is an equation that makes a straight line when graphed. It has the form ax + by = c, where a, b, and c are constants.

Tags

CCSS.HSF.LE.A.2

CCSS.8.F.B.4

Front

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

Back

A consistent system has at least one solution, meaning the lines 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 lines are parallel and never intersect.

Tags

CCSS.8.EE.C.8B

Front

What is the graphical method of solving a system of equations?

Back

The graphical method involves graphing each equation on the same set of axes and identifying the point(s) of intersection.

Tags

CCSS.8.EE.C.8B

Front

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

Back

Substitute the solution back into the original equations to verify that both equations are satisfied.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What is a word problem in the context of systems of equations?

Back

A word problem is a real-life scenario that can be modeled using a system of equations to find unknown values.

Tags

CCSS.8.EE.C.8C

Front

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

Back

Identify the unknowns, create equations based on the relationships described in the problem, and express them in terms of the unknowns.

Tags

CCSS.8.EE.C.8C