Test Review: 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.

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.

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.

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.

Front

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

Back

An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

Front

What is the definition of a dependent system of equations?

Back

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

Front

How can you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure they reflect the problem's constraints.

Front

What is the cost of one nacho if Charlie sold 35 nachos and 52 sodas for a total of $78.50?

Back

$1.50 per nacho.

Front

If Wyatt spent $175 on 7 shirts and 7 shorts, what is the cost of one shirt?

Back

$10 per shirt.

Front

What system of equations represents Nancy's grocery purchases?

Back

4x + 6y = 13 and 3x + 7y = 13.50, where x is the cost of an apple and y is the cost of a banana.