Systems of Equations- Graphing & 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

What does it mean to solve a system of equations by graphing?

Back

To solve a system of equations by graphing means to plot the equations on a graph and identify the point(s) where they intersect, which represents the solution.

Front

What is the solution to the system of equations y = 1/2x + 2 and y = -3x + 9?

Back

(2, 3)

Front

How can you determine the number of solutions in a system of equations?

Back

You can determine the number of solutions by analyzing the graphs: if they intersect at one point, there is one solution; if they are parallel, there is no solution; if they are the same line, there are infinitely many solutions.

Front

What is the setup fee in the shirt company problem?

Back

The setup fee is the fixed cost charged by the company before any shirts are ordered.

Front

Write the equations for the two shirt companies based on the problem: One charges $9.65 per shirt plus a setup fee of $43, and the other charges $8.40 per shirt plus a $58 fee.

Back

y = 9.65x + 43 and y = 8.40x + 58.

Front

What does it mean if a system of equations has no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

In the candle selling problem, how do you find the number of candles Jane and Chris need to sell to earn the same profit?

Back

Set their profit equations equal to each other and solve for the number of candles.

Front

What is the profit equation for Jane if she sells candles for $3 each after spending $20?

Back

Profit = 3x - 20, where x is the number of candles sold.

Front

What is the profit equation for Chris if he sells candles for $5 each after spending $40?

Back

Profit = 5x - 40, where x is the number of candles sold.