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

<p>Graph of a line in the x y plane, origin O, with grid. Horizontal axis, scale negative 6 to 6, by 1’s. Vertical axis, scale negative 6 to 6, by 1’s. The line crosses the y axis at 4. It passes through the point 4 comma 1.</p>  

Write a second equation for the system so that:

1. The system has infinitely many solutions.
2. The system has no solutions, and the line representing the new equation goes through the point \((0,1)\).
3. The system has a solution at \((4,1)\), and the line representing the new equation goes through the point \((0,2)\).

Create a second equation so the system has no solutions.

\(\begin{cases} y=\dfrac34x -4 \\[5ex] \\[2ex] \end{cases}\)

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.

<p>The graph of two intersecting lines in the x y plane. The first line slants downward and right and passes through the point 4 comma 5 point 5. The second line slants downward and to the right and passes through the point 5 comma 5. The lines intersect at the point 6 comma 4.</p>  

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?

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

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 \(\text-60\) degrees Fahrenheit. How many degrees Celsius is this?
3. Diego’s cousin claims that -40 degrees Celsius is the same temperature as -40 degrees Fahrenheit. Check that this is true.