Systems of Equations
Here is the graph for one equation in a system of equations:
Description: <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 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 \((4,1)\).
Create a second equation so the system has no solutions.
\(\begin{cases} y=\frac34x -4 \\ \\ \end{cases}\)
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.
Description: <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>
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?
The temperature in degrees Fahrenheit, \(F\), is related to the temperature in degrees Celsius, \(C\), by the equation \(\displaystyle F = \frac{9}{5}C + 32\)
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.