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?
Solution 1
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).
To learn more about the linear system of an equations visit:
brainly.com/question/27664510.
#SPJ3
Solution 2
Answer:
(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
One gallon holds eight pints. 8 x 3 = 24
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
To learn more about circle click :
#SPJ3
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
3x-11 = -3x-2
add 3x on both sides
6x-11 = -2
add 11 on both sides
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!!!
Answer:
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
8 ×
Now to make the calculation easier,, factor the expression.
(8 ×
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
Lastly,, multiply the numbers together to get your final answer.
7999800
This means that 8 ×
Let me know if you have any further questions.
:)
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!
hope this helps
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
Answer:
$1248.
Step-by-step explanation:
area = base x height.
then
area x cost
b h c
32 x 15 x 2.6 = 1248