Question

question 1. •the quilter needs at least 9.5 yards of fabric in total.•the blue fabric costs $9 a yard.•The green fabric costs $13.• the quilter can spend up to $110 on fabricthe inequalities to represent the constraints in this situation are :x + y ≥ 9.59x + 13y ≤ 110

Answer 1

We graph it as follows:

We will have that a solution for both systems is found at the intersection.

*One of the solutions can be 10 yards of blue fabric and 1 yard of green fabric. [Theare are multiple solutions for the system] //We also know that the solutions are all positive [Since we are talking about quantities].

*Another solution can be 6 yards of blue fabric and 4 yards of green fabric.

**We can determine they are solutions since they are the intersections of integers that are contained at the intersection of solutions for the inequalities.

***The solutions given replaced in the equations:

*First set.

$10+1\ge9.5\Rightarrow11\ge9.5$$9(10)+13(1)\le110\Rightarrow103\le110$

*Second set:

$6+4\ge9.5\Rightarrow10\ge9.5$$9(6)+13(4)\le110\Rightarrow106\le110$