Question

I WILL GIVE BRAINLIEST AND POINTS! Plz help me with this question. Help with part C plz

Answer 1

Answer:

First solve the two inequalities by putting them in function format:

$2x + y \leq 8\\y\leq -2x+8$      $x + y\geq 4\\y\geq -x+4$

Part A:

For the inequality $2x+y\leq 8$ , the solution set would be the area under the graphed line of $y=-2x+8$, where the y-values are smaller, since it asks for y is smaller than or equal to $-2x+8$. Because it is a $\leq$, the line would be filled, not dotted, and the points on the line would also be included in the solution.

For the inequality $x+y\geq 4$, the solution set would be the area above the graphed line of $y=-x+4$, where the y-values are larger, since it asks for y is larger than or equal to $-x+4$. Because it is a $\geq$, the line would be filled, not dotted, and the points on the line would also be included in the solution.

The solution set that met both inequalities would be the area on the graph that covers the solution for both inequalities. The y-values has to be smaller than or equal to $-2x+8$, but greater than or equal to $-x+4$, meaning they lie within the range of $4-x\leq y\leq 8-2x$. It would be the area double-shaded on the graph.

Part B:

Substitute in the point (8, 10) into both inequalities and see if it's true:

$y\leq -2x+8\\10\leq -2(8)+8\\10\leq 8-16\\10\leq -8$       $y\geq -x+4\\10\geq -(8)+4\\10\geq 4-8\\10\geq -4$

Even though it's true in the inequality $y\geq -x+4$, it's false in the inequality $y\leq -2x+8$ because 10 is not smaller than -8. Therefore the point (8, 10) is not included in the solution area for the system.

Part C:

A point within the solution would be the intersection point of $y=-2x+8$ and $y=-x+4$. Therefore, set those two functions equal to each other to find the coordinates of intersection:

$-2x+8=-x+4\\x-2x=4-8\\-x=-4\\x=4$        $y=-x+4\\y=-(4)+4\\y=4-4\\y=0$        $y=-2x+8\\y=-2(4)+8\\y=8-8\\y=0$

The intersection point and a solution to the system of inequality would be (4, 0). This means Sarah can buy 4 cupcakes and 0 fudge, while meeting her budget of $8 and being able to feed at least four siblings.