# Lesson 12

Systems of Equations

Let’s learn what a system of equations is.

### Problem 1

Here is the graph for one equation in a system of equations:

1. Write a second equation for the system so it has infinitely many solutions.
2. Write a second equation whose graph goes through $$(0,1)$$ so the system has no solutions.
3. Write a second equation whose graph goes through $$(0,2)$$ so the system has one solution at $$(4,1)$$.

### Problem 2

Create a second equation so the system has no solutions.

$$\begin{cases} y=\frac34x -4 \\ \\ \end{cases}$$

### Problem 3

Andre is in charge of cooking broccoli and zucchini for a large group. He has to spend all $17 he has and can carry 10 pounds of veggies. Zucchini costs$1.50 per pound and broccoli costs $2 per pound. One graph shows combinations of zucchini and broccoli that weigh 10 pounds and the other shows combinations of zucchini and broccoli that cost$17.

1. Name one combination of veggies that weighs 10 pounds but does not cost $17. 2. Name one combination of veggies that costs$17 but does not weigh 10 pounds.
3. How many pounds each of zucchini and broccoli can Andre get so that he spends all \$17 and gets 10 pounds of veggies?
(From Unit 4, Lesson 10.)

### Problem 4

The temperature in degrees Fahrenheit, $$F$$, is related to the temperature in degrees Celsius, $$C$$, by the equation $$\displaystyle F = \frac{9}{5}C + 32$$

1. In the Sahara desert, temperatures often reach 50 degrees Celsius. How many degrees Fahrenheit is this?

2. In parts of Alaska, the temperatures can reach -60 degrees Fahrenheit. How many degrees Celsius is this?

3. There is one temperature where the degrees Fahrenheit and degrees Celsius are the same, so that $$C=F$$. Use the expression from the equation, where $$F$$ is expressed in terms of $$C$$, to solve for this temperature.

(From Unit 4, Lesson 9.)