Lesson 12: Practice Problems

Problem 1

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

A coordinate grid with a line intersecting the y axis at (0, 4) .

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

${\begin{cases} y = \frac{3}{4} x - 4 \end{cases}$

Problem 3 From Unit 4 Lesson 10

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.

A graph of zucchini (pounds) vs broccoli (pounds) with two line that intersect at (6,4).

Name one combination of veggies that weighs 10 pounds but does not cost $17.
Name one combination of veggies that costs $17 but does not weigh 10 pounds.
How many pounds each of zucchini and broccoli can Andre get so that he spends all $17 and gets 10 pounds of veggies?

Problem 4 From Unit 4 Lesson 9

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

In the Sahara desert, temperatures often reach 50 degrees Celsius. How many degrees Fahrenheit is this?
In parts of Alaska, the temperatures can reach -60 degrees Fahrenheit. How many degrees Celsius is this?
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.