Which system of equations is satisfied by the solution shown on the graph?

Answer:

D

Step-by-step explanation:

To find the system of equations that is satisfied by the solution shown on the graph, we will simply need to find the equations of our two lines.

So, we will begin by finding the slope of each line and then proceed to find the entire equation.

Red Line:

To find the slope, we will first pick any two points from the red line.

Two sample points include (-5, 5) and (-4, 6).

The slope formula is given by:

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Lett (-5, 5) be (x₁, y₁) and (-4, 6) be (x₂, y₂). Substitute:

[tex]\displaystyle m=\frac{6-5}{-4-(-5)}=\frac{1}{1}=1[/tex]

Hence, the slope of the red line is 1.

Now, we can find the entire equation. We will use the slope-intercept form:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

We know that the slope m is 1. Hence:

[tex]y=x+b[/tex]

We need to find our y-intercept b. For the red line, we know that when x is -5, y is 5. Hence:

[tex](5)=(-5)+b[/tex]

Solving for b yields:

[tex]b=10[/tex]

Therefore, our entire equation is:

[tex]y=x+10[/tex]

Blue Line:

Again, we will find the slope first.

Picking two points, we get (0, 6) and (1, 5).

Using the slope formula by letting (0, 6) be (x₁, y₁) and (1, 5) be (x₂, y₂), we acquire:

[tex]\displaystyle m=\frac{5-6}{1-0}=\frac{-1}{1}=-1[/tex]

Hence, the slope of the blue line is -1.

Again, we can use the slope-intercept form:

[tex]y=mx+b[/tex]

Fortunately, we already know the y-intercept in this case. Since we have the point (0, 6), the y-intercept b is 6.

Therefore, our equation is:

[tex]y=-x+6[/tex]

So, our two equations are:

[tex]y=x+10\text{ and } y=-x+6[/tex]

Our answers are in standard form, so we will convert the two equations to standard form. Standard form is given by:

[tex]Ax+By=C[/tex]

Where A, B, and C are integers and A is positive.

For the first equation, we can subtract x from both sides to get:

[tex]-x+y=10[/tex]

Since A should be positive, we multiply both sides to get:

[tex]x-y=-10[/tex]

For the second equation, we can add x to both sides:

[tex]x+y=6[/tex]

Hence, our two equations in standard form is:

[tex]x+y=6\text{ and } x-y=-10[/tex]

Therefore, our final answer is D.

Answer: D x + y = 6 and x − y = -10

Step-by-step explanation:

What is the ratio 28 : 35 written in lowest terms?
A.9: 15
B.7:19
C.4:5
D.3:7​

someone please solve and find the corresponding angles thanks

I need help with this​

Even if you don’t think it is an independent variable, _____ is usually always plotted on the “x” axis.


Help?

I need help one this question.

How do I solve this equation by completing the square. 4X^2 + 12x +5 = 21

If x to the first power is a line, and you multiply two lines together, what do you get? Think of the the exponent.

quick!! write an equation in slope intercept form using points (-3,0) (3,-4) !

The obriens are buying new windows for their house. The company installs the new windows for 2100 the total cost for buying the windows and having them installed is 5323.50 of the o'briens pay 230.25 per window how many windows did they buy

Which value of x makes the equation x + 7 = 21 true?
O A. 7
O B. 14
O c. 21
OD. 28

What is 149/15 as a mixed number?

If a 70 kg person on a 15 kg sled is pushed with a force of 300 N, what will be person's
acceleration?

A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 420 feet. Determine the​ flag's length and width if the length is 110 feet greater than the width. Use pencil and paper. Write three situations to which you could apply the resulting system of equations.
What is the length of the flag?

y = m + mnp
Solve for n.
pls help me

PLEASE I NEED AN ANSWER NOW WILL MARK U BRAINLIEST!!!1!
how do u find y intercept without a graph for systems of equations? (y = x - 6)

can you please help me with this​

transversals angles​

what is the quotient of 6 1/4 ÷ (-5/8)​

v=u + at
u= 2
a= -5
t = 1/2
Work out the value of v.

In a football stadium, 43% of the crowd cheering for Team A, and 52% of the crowd is female. 19% of the crowd is cheering for Team A and female . What is the probability that a randomly selected Person from the crowd are cheering for Team A or female?

EEEEEEEEEEEEEEEEEEEEEEEE

Find two numbers with sum 82 and difference 30.

PLEASE ANSWER! 15 POINTS

The total cost of renting a banquet hall is a function of the number of hours the
hall is rented. The owner of the banquet hall charges $45 per half hour up to a
maximum of 5 hours and a $50 cleaning fee. The equation used to express the
situation is C = 45h + 50, where h is the number of half hours. What is the
greatest value in the range for this situation?

please help me i don’t understand how to do this

15PTS PLEASE HELP ASAP!
(dont write random answers pls))

Which table does NOT show y as a function of x?

can someone help me understand this ​

SOMEONE ANWSER QUICK !

If you want to solve the system of equations below using the elimination methiod, which of the following should NOT be
your first step:

-3x + 4y = 0
2 - 2y = 8

A)Multiply every term in the bottom equation by 3.

B) Multiply every term of the bottom equation by 2.

C) Multiply every term of the bottom equation by -3.

D Multiply every term of the top equation by 2, and every term of the bottom equation by 4.

can someone answer the questions on my page if so ill give all the correct answers brainlist.