The graph of the system of inequalities is a shaded region in the first quadrant of the coordinate plane.
The line 7x + 3y = 42 represents all the possible combinations of colored pen sets and notebooks that Tyler can purchase with his $42 budget. The line starts at the point (0, 14) on the y-axis and has a slope of -7/3. This means that for every increase of 3 in y, the value of x will decrease by 7.
Since x and y represent the number of colored pen sets and notebooks, respectively, x ≥ 0 and y ≥ 0 represent non-negative values for these variables. This means that we can only consider the points in the first quadrant of the coordinate plane.
The shaded region below the line 7x + 3y = 42 and within the first quadrant of the coordinate plane satisfies all the conditions of the system of inequalities. This shaded region represents all the possible combinations of colored pen sets and notebooks that Tyler can purchase with his $42 budget and within the given constraints.
Please note that without any specific values for x and y, it is not possible to determine the exact shape and position of the shaded region.
Tyler has $42 to spend on art supplies. Colored pen sets cost $7 and notebooks cost $3.
Let x
represent the number of colored pen sets.
Let y
represent the number of notebooks.
7x+3y≤42
x≥0
y≥0
This is the graph of the system of inequalities.
1 answer