Mathematics, 23.07.2019 03:20 Valduarte07

The common point between lines y = 2x + 5 and y = ½ x + 6 is (3, 1/2).

Answers: 2

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Answer from: genyjoannerubiera

The ordered pair (3,1/2) is not a common point, the statement is false

The solution is the point (0.667, 6.333) (common point)

Step-by-step explanation:

we have

y=2x+5 -----> equation A

$y=\frac{1}{2}x+6$ ----> equation B

we know that

If a ordered pair is a common point between the two lines,

then

the ordered pair must satisfy both equations

step 1

Verify if the ordered pair (3,1/2) satisfy equation A

substitute the value of x and the value of y in the equation A and then compare the results

For x=3, y=1/2

$\frac{1}{2}=2(3)+5$

$\frac{1}{2}=11$ ----> is not true

The ordered pair don't satisfy the equation A

therefore

The ordered pair is not a common points both lines

The statement is false

step 2

Find the common point between the two lines

y=2x+5 -----> equation A

$y=\frac{1}{2}x+6$ ----> equation B

Solve the system of equations by graphing

The intersection point both graphs is the solution of the system (common point)

using a graphing tool

The solution is the point (0.667, 6.333) (common point)

see the attached figure

The common point between lines y = 2x + 5 and y = ½ x + 6 is (3, 1/2).

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

Answer from: Quest

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step-by-step explanation:

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