Mathematics, 16.07.2019 12:30 heber9609

Which ordered pairs are in the solution set of the system of linear inequalities? y > -1/2x y < 1/2x + 1 a (5, –2), (3, 1), (–4, 2) b (5, –2), (3, –1), (4, –3) c (5, –2), (3, 1), (4, 2) d (5, –2), (–3, 1), (4, 2)

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The solution set of C works for both equations.

You can find this by looking for true statements when you put each of the ordered pairs into each of the equations.

Ordered Pair #1 (5, -2)
y > -1/2x
-2> -1/2(5)
-2> -2.5 (TRUE)

y < 1/2x + 1
-2 < 1/2(5) + 1
-2 < 2.5 + 1
-2 < 3.5 (TRUE)

Ordered Pair #2: (3, 1)
y > -1/2x
1 > -1/2(3)
1> -1.5 (TRUE)

y < 1/2x + 1
1 < 1/2(3) + 1
1 < 1.5 + 1
1 < 2.5 (TRUE)

Ordered Pair #3: (4,2)
y > -1/2x
2 > -1/2(4)
2 > -2 (TRUE)

y < 1/2x + 1
2 < 1/2(4) + 1
2 < 2 + 1
2 < 3 (TRUE)

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Answer from: Quest

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

=3x+1

=3(2)+1

since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

=x+1

=2+1

now, let's find g(2)g(2):

g(x)

g(2)

=2x

=2⋅2

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

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