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bagirrra123 [75]
3 years ago
10

What system of inequalities is represented by the graph?

Mathematics
1 answer:
yarga [219]3 years ago
7 0
As shown in the figure, we have two straight line. One of them has a negative slope and the other has a positive one. In two dimensions, the equation for non-vertical lines is often given in the slope-intercept form by:

y=mx+b

being m the slope of the line and <span>b the y-intercept of it.

On the other hand, if x = 0 then y = b.

First of all we will order the equations above without </span>inequalities<span> like this:

A. </span>y = 5x-1, y = 3x+4
<span>B. </span>y = 5x-1, y = -3x+4
C. y = 5x+1, y = -3x+4
D. y = 5x-1, y = -3x-4<span>

 As shown in the figure b = -1 for one straight and b = 4 for the second one. This values take place when x = 0. So, we discard C and D, because if x = 0, then:
</span>
For C, b = 1 and b = 4
For D, b = -1 and b = -4

Let's analyze A and B. So:

For A, m = 5 and m = 3
For B, m = 5 and m = -3

Therefore, we discard A because of the statement above.

Finally the answer is B. So, the inequalities are:  

(1) y\ \textless \ 5x-1
(2) 3x+y \geq 4

Let's prove this answer. We will take the point (2, 0) that is in the region in gray. So, substituting this point in the inequalities, we have:

(1) 0\ \textless \ 9
(2) 6 \geq 4

In fact, this is true.


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