Writing Systems of Equations

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations that have the same variables.

Front

Solve for y: 4x + 3y = 9

Back

y = -4/3x + 3

Front

If Alexandra can give 3 haircuts and 2 hair dyes in 315 minutes, and 2 haircuts and 4 hair dyes take 450 minutes, what system of equations represents this situation?

Back

3H + 2D = 315, 2H + 4D = 450

Front

Christian ordered 4 boxes of black-and-white brochures and 3 boxes of color brochures for $134. After that, he spent $120 on 3 boxes of black-and-white and 3 boxes of color brochures. What system represents this situation?

Back

4x + 3y = 134, 3x + 3y = 120

Front

The talent show committee sold 530 tickets in advance. Student tickets cost $3 each and adult tickets cost $4 each. What system can be used to find how many of each type of ticket were sold?

Back

S + A = 530, 3S + 4A = 1740

Front

What does it mean to solve a system of equations?

Back

To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

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.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is a consistent system of equations?

Back

A consistent system of equations has at least one solution.

Front

What is an inconsistent system of equations?

Back

An inconsistent system of equations has no solutions.