Mathematics, 12.10.2019 00:30 Alex4530

What is the solution to the system of equations below?
y=1/2x+6 and y=3/4x-4

a. (–8, 2)
b. (–8, –1)
c. (8, 10)
d. (8, –10)

Answers: 3

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Answer from: candlewax2001

A. (–8, 2)

Step-by-step explanation:

(1) y = ½x + 6

(2) y = -¾x – 4 Set (1) = (2)

½x + 6 = -¾x – 4 Multiply each side by 4

2x + 24 = -3x – 16 Add 16 to each side

2x + 40 = -3x Subtract 2x from each side

40 = -5x Divide each side by -5

(3) x = -8 Substitute (2) into (1)

y = ½(-8) +6

= -4 + 6

= 2

The solution to the system of equations is (-8 ,2).

You can see the graphs of the two functions in the figure below. The two lines intersect at (-8, 2).

Check:

2 = ½(-8) + 6 2 = -¾(-8) - 4

2 = -4 +6 2 = 6 - 4

2 = 2 2 = 2

What is the solution to the system of equations below? y=1/2x+6 and y=3/4x-4 a. (–8, 2) b. (–8, –1

Answer from: Quest

your answer is b ^w^ hope i

Which could be a conditional relative frequency table ?

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.

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What is the solution to the system of equations below?
y=1/2x+6 and y=3/4x-4

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