# Two lines, C and D, are represented by the equations given below: Line C: y = x + 14 Line D: y = 3x + 2 Which of the following shows the solution to the system of equations and explains why?

2 months ago

## Solution 1

Guest #3231
2 months ago

The solution for the given system of equations are (6, 20).

### What is a linear system of equations?

A system of linear equations is a set of two or more equations involving two or more variables. All of the equations must be considered at once in order to find the solution, which is any pair of values that makes each equation true independently.

The given system of linear equations are y=x+14 -----(i) and y=3x+2 -----(ii).

From equation (i) and (ii), we get

x+14=3x+2

3x-x=14-2

2x=12

x=6

Substitute x=6 equation (i), we get

y=20

Therefore, the solution for the given system of equations are (6, 20).

#SPJ3

## Solution 2

Guest #3232
2 months ago

(6, 20), because both lines pass through this point

Step-by-step explanation:

We see that both equations are equal to y.  This means we can set the two equations equal to each other:

x+14 = 3x+2

Subtract x from each side:

x+14-x = 3x+2-x

14 = 2x+2

Subtract 2 from each side:

14-2 = 2x+2-2

12 = 2x

Divide both sides by 2:

12/2 = 2x/2

6 = x

Substitute this into the first equation:

y = x+14

y = 6+14

y = 20

This makes the solution (6, 20).

## 📚 Related Questions

Question
Fernando poured water from one-pint bottles into a three-gallon bucket. How many pints of water could the bucket hold?
Solution 1
Solution 2
24

One gallon holds eight pints. 8 x 3 = 24
Question
The diameter of a DVD is 12 centimeters. The hole in the center of a DVD has a diameter of 1.5 centimeters. Find the area of the DVD. Round to the nearest hundredth if necessary.
Solution 1

The area of the circular DVD is given by A = 111.33 cm²

### What is a Circle?

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the area of the circular DVD be A

Let the diameter of the DVD = 12 cm

So , the radius of the DVD = 6 cm

Now , the diameter of the hole = 1.5 cm

So , the radius of the hole = 0.75 cm

And , area of the circular DVD be A = π [ ( 6 )² - ( 0.75 )² ]

On simplifying , we get

The area of circular DVD is A = π ( 36 - 0.5625 )

The area of circular DVD is A = π ( 35.4375 )

The area of circular DVD is A = 111.33 cm²

Hence , the area of the circular DVD is 111.33 cm²

brainly.com/question/28391204

#SPJ3

Solution 2
111.27 centimeter squared.
Question
Y=3x - 11 Y= -3x - 2
Solution 1
Subsitution method.

Y=3x - 11
Y= -3x - 2

-3x - 2 = 3x - 11
+3x        +3x

-2 = 6x - 11
+11       +11

6x = 9
x = 1.5

Y=3(1.5) - 11
y = 4.5 - 11
y = -6.5

Now we have our points.

Answer: x = 1.5 and y = -6.5
Solution 2
Well, you do Equality method.

3x-11 = -3x-2

6x-11 = -2

6x = 9
divide 6 on both sides

x = 3/2

As you found the x value, you now need to find the y value by plugging in the x value in one of the above equations and solve for y.

y = 3x-11
y = 3(3/2) -11
y = 9/2 -11
y = -13/2

So, the answer is (3/2,-13/2) or (1.5,-6.5)

HOPE THIS HELPS!!!
Question
The sum of 5 consecutive integers is 270
Solution 1
54+54+54+54+54=270 270 divided by 5 is 54
Question
What must you do if you multiply one number in a ratio by n?
Solution 1

multiply the others by n

Step-by-step explanation:

If you want to keep the same ratio, you must multiply all of the numbers by n.

A ratio of 1 : 1 will remain 1 : 1 if all the numbers are multiplied by n:

1 : 1 = n : n

_____

Comment on alternate interpretation of the question

There are occasions for multiplying the ratio by n:

x/n = 1/2

To solve this for x, we multiply the ratio (1/2) by n. This multiplies the numerator, but does not change the denominator.

x = n(1/2) = n/2

Question
The ___ is the collection of all possible individual outcomes for a chance process. The total probability of all the possible individual outcomes is ____. Choices for first blank: probability model; relative frequency; sample space; probability Choices for second blank: 0.5; 0; 1; 100
Solution 1
0.5 is it i had this question before
Question
How many times larger is 8*10^6 than 2*10^2
Solution 1
The first step for solving this question is put both of your given expressions into one and then subtract them. This will look like the following:
8 ×  - 2 × 10²]
Now to make the calculation easier,, factor the expression.
(8 ×  - 2) × 10²
Evaluate the power inside the parenthesis.
(8 × 10000 - 2) × 10²
Evaluate the power outside the parenthesis.
(8 × 10000 - 2) × 100
Multiply the numbers inside the parenthesis.
(80000 - 2) × 100
Subtract the numbers in the parenthesis.
79998 × 100
7999800
This means that 8 ×  is 7999800 times larger than 2 × 10².
Let me know if you have any further questions.
:)
Question
If x is to 6 as 10 is to 15, then x is equal to
Solution 1
The answer you are looking for is X = 4.

To find this, you must first figure out the relationship between 10 and 15. Since 10 is 2/3 of 15, "x" must be 2/3 of 6.

To find "x", divide 6 by 3 to get 2, then 2 by 2 to get 2/3 of 6 (4). Thus meaning X = 4.

I hope this helps!
Question
A bag of apples weighs 7 7/8 pounds. By weight, 1/18 of the apples are rotten.what is the weight of the good apples
Solution 1
The answer would be 6 1/4 apples

hope this helps
Question
A lawn is shaped like a parallelogram with a base of 32 feet and a height of 15 feet. Covering the lawn with grass will cost \$2.60 per square foot. How much money will it cost to cover the lawn with grass?
Solution 1
The total cost would be \$1248.

To find the total cost, we need to first find the area of the parallelogram. To find the area, we need to multiply the base and height.

Then, we need to multiply the total area by the cost of \$2.60.

32 x 15 x 2.6 = 1248
Solution 2

\$1248.

Step-by-step explanation:

area = base x height.

then

area x cost

b       h      c

32 x 15 x 2.6 = 1248

2647929
842281
748681
586256
406852
368373
348603
324927
199835
130075
112100
106146
77164
23213
22589
19607
17108
13966
10987
3389