Mathematics, 05.07.2019 12:30, RyanODON

Which graph represents the solution set of the system of inequalities? {x+y< 12 y≥x−4

Answers: 2

Show answers

Answers

answered: lanaiheart7

Inequalities are used to relate unequal expressions.

See attachment for the graph that represents the solution set

The inequalities are given as:

$\mathbf{x + y < 12}$

$\mathbf{y \ge x - 4}$

Assume the inequalities are equations

$\mathbf{x + y = 12}$

$\mathbf{y = x - 4}$

Substitute $\mathbf{y = x - 4}$ in $\mathbf{x + y = 12}$

$\mathbf{x + x - 4 =12}$

$\mathbf{2x - 4 =12}$

Collect like terms

$\mathbf{2x = 4 +12}$

$\mathbf{2x = 16}$

Divide both sides by 2

$\mathbf{x = 8}$

Substitute $\mathbf{x = 8}$ in $\mathbf{y = x - 4}$

$\mathbf{y = 8 - 4}$

$\mathbf{y = 4}$

Back to the inequalities:

$\mathbf{x + y < 12}$

$\mathbf{y \ge x - 4}$

The solution to the inequalities would be:

$\mathbf{x < 8}$

$\mathbf{y \ge 4}$

$\mathbf{x < 8}$ and $\mathbf{x + y < 12}$ means that:

The line of the graph passes through x = 12 with a dotted lineThe left-hand side of the graph is shaded

$\mathbf{y \ge 4}$ and $\mathbf{y \ge x - 4}$ means that:

The line of the graph passes through y = -4 with a solid lineThe upper side of the graph is shaded

None of the given graphs represent the solution to the inequalities

See attachment for the graph that represents the solution set of the system of inequalities

Read more about inequalities at:

link

Which graph represents the solution set of the system of inequalities? {x+y< 12 y≥x−4

answered: lizzepacheco

The graph in the bottom right-hand corner

(see figure 4 in the attached images below)

===========================================

Explanation:

Let's start off by graphing x+y < 1. The boundary equation is x+y = 1 since we simply change the inequality sign to an equal sign. Solve for y to get x+y = 1 turning into y = -x+1. This line goes through (0,1) and (1,0). The boundary line is a dashed line due to the fact that there is no "or equal to" in the original inequality sign. So x+y < 1 turns into y < -x+1 and we shade below the dashed line. The "less than" means "shade below" when y is fully isolated like this. See figure 1 in the attached images below.

Let's graph 2y >= x-4. Start off by dividing everything by 2 to get y >= (1/2)x-2. The boundary line is y = (1/2)x-2 which goes through the two points (0,-2) and (4,0). The boundary line is solid. We shade above the boundary line. Check out figure 2 in the attached images below.

After we graph each individual inequality, we then combine the two regions on one graph. See figure 3 below. The red and blue shaded areas in figure 3 overlap to get the purple shaded area you see in figure 4, which is the final answer. Any point in this purple region will satisfy both inequalities at the same time. The solution point cannot be on the dashed line but it can be on the solid line as long as the solid line is bordering the shaded purple region. Figure 4 matches up perfectly with the bottom right corner in your answer choices.

answered: Guest

idk im srry

step-by-step explanation:

answered: Guest

answer: plz give a pic and answer choices so i can answer!

step-by-step explanation:

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 13:30, jamesgraham577

Which transformations could have occurred to map △abc to △a"b"c"? a rotation and a reflection a translation and a dilation a reflection and a dilation a dilation and a rotation

Answers: 1

continue

Mathematics, 21.06.2019 21:30, Harriche

The perimeter of a rectangular lot of land is 436 ft. this includes an easement of x feet of uniform width inside the lot on which no building can be done. if the buildable area is 122 ft by 60 ft, determine the width of the easement. select one: a. 9 feet b. 18 feet c. 4.5 feet d. 7 feet

Answers: 3

continue

Mathematics, 21.06.2019 22:00, jnkbragg3696

Problem situation: caren is making rice and beans. she can spend no more than $10 on ingredients. she buys one bag of rice for $4.99. beans cost $0.74 per pound. how many pounds of beans, x, can she buy? inequality that represents this situation: 10≥4.99+0.74x drag each number to show if it is a solution to both the inequality and the problem situation, to the inequality only, or if it is not a solution.

Answers: 1

continue

Mathematics, 21.06.2019 22:30, idontknow1993

What would be the reasons for lines 3 and 4? a. addition property; subtraction property b. addition property; solve c. substitution property; subtraction property d. substitution property; prove

Answers: 1

continue

Do you know the correct answer?

Which graph represents the solution set of the system of inequalities? {x+y< 12 y≥x−4...