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