Systems 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.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. 4. Substitute back to find the first 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

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

Back

A consistent system has at least one solution, meaning 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 equations do not intersect at any point.

Tags

CCSS.8.EE.C.8B

Front

What is a dependent system of equations?

Back

A dependent system has infinitely many solutions, meaning the equations represent the same line.

Tags

CCSS.8.EE.C.8B

Front

How can you represent a system of equations graphically?

Back

You can graph each equation on the same coordinate plane. The point(s) where the lines intersect represent the solution(s) of the system.

Tags

CCSS.8.EE.C.8B

Front

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

Back

Identify the variables that represent the unknown quantities in the problem.

Tags

CCSS.8.EE.C.8C

Front

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

Back

Break down the problem into mathematical statements based on the relationships described in the text.

Tags

CCSS.8.EE.C.8C

Front

What is the importance of checking your solution in a system of equations?

Back

Checking your solution ensures that it satisfies all equations in the system, confirming its validity.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6