How will the solution of the system change if the inequality sign on both inequalities

Question

30-06-2019
Mathematics

contestada

How will the solution of the system change if the inequality sign on both inequalities

Respuesta :

Otras preguntas

A conical tank (as in Example 2) has height 3 m and radius 2 m at the base. Water flows in at a rate of 2 m3/min. How fast is the water level rising when the le

If an administrator wanted to change the IP configuration settings on the first Ethernet interface to 10.1.1.1 and the netmask to 255.255.255.0, what is the com

The local deli charges a fee for delivery. On monday, they delivered two dozen bagels to an office at a local cost of $8. On Tuesday, three dozen bagels were de

An electric current is trying to move through an atom. How do protons an electrons impact the movement of electricity

A lottery game requires a person to select two upper case letters and three differentnon-zero digits. How many choices can the customer make? You may leave your

The lionfish is an invasive species from the Indo-Pacific, now also found in the East Coast of the United States and in the Caribbean. An exceptional predator t

A recent study of 100 employees from six departments of a major corporation found 65% to be sleep deprived. The researchers concluded that the majority of corpo

PLZ HELP IT'S DUE TOMORROW!!!! I'LL GIVE BRAINLIEST TO FIRST CORRECT ANSWER AND ALL MY POINTS The sum of a sequence of consecutive integers is 342. The largest

Which statement best describes the relationship of photosynthesis and energy? The process of photosynthesis is energy-storing because the process converts light

WFO Corporation has gross receipts according to the following schedule: Year 1 $2 million Year 2 $4 million Year 3 $6 million Year 4 $4.5 million Year 5 $5 mill

danielmaduroh danielmaduroh · Answer 1 · 2019-07-01T23:38:12+02:00

Answer:

Shown below

Step-by-step explanation:

The first system of inequality is the following:

[tex]\left\{ \begin{array}{c}y>2x+\frac{2}{3}\\y<2x+\frac{1}{3}\end{array}\right.[/tex]

To find the solution here, let's take one point, say, [tex](0,0)[/tex] and let's taste this point into both inequalities, so:

FIRST CASE:

First inequality:

[tex]y>2x+\frac{2}{3} \\ \\ 0>2(0)+\frac{2}{3} \\ \\ 0>\frac{2}{3} \ False![/tex]

The region is not the one where the point [tex](0,0)[/tex] lies

Second inequality:

[tex]y<2x+\frac{1}{3} \\ \\ 0<2(0)+\frac{1}{3} \\ \\ 0<\frac{1}{3} \ True![/tex]

The region is the one where the point [tex](0,0)[/tex] lies

So the solution in this first case has been plotted in the first figure. As you can see, there is no any solution there

SECOND CASE:

First inequality:

[tex]y<2x+\frac{2}{3} \\ \\ 0<2(0)+\frac{2}{3} \\ \\ 0<\frac{2}{3} \ True![/tex]

The region is the one where the point [tex](0,0)[/tex] lies

Second inequality:

[tex]y>2x+\frac{1}{3} \\ \\ 0>2(0)+\frac{1}{3} \\ \\ 0>\frac{1}{3} \ True![/tex]

The region is not the one where the point [tex](0,0)[/tex] lies

So the solution in this first case has been plotted in the second figure. As you can see, there is a solution there.

CONCLUSION: Notice that when reversing the signs on both inequalities the solution in the second case is the part of the plane where the first case didn't find shaded region.