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3 years ago

What is the solution of the system? 5x + 2y = 9 4x - 3y = 44

Mathematics

1 answer:

Lady bird [3.3K]3 years ago

6 0

Hello!

$\large\boxed{5, -8}$

5x + 2y = 9

4x - 3y = 44

We can eliminate y by multiplying both expressions in order to have the y coefficients equal.

The LCM (least common multiple) of 2 and 3 is 6, so we can multiply each accordingly:

3(5x + 2y = 9)

2(4x - 3y = 44)

Distribute:

15x + 6y = 27

8x - 6y = 88

Cancel using addition:

15x + 6y = 27

8x - 6y = 88

------------------

23x = 115

Divide:

x = 5.

Plug in this value of x into an equation to solve for y:

5(5) + 2y = 9

25 + 2y = 9

2y = -16

y = -8

The solution of the system is:

(5, -8).

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Which of the following is a true equation?<br> k=y/x<br> k= x/y<br> x= y/k

faust18 [17]

Answer:

Step-by-step explanation:

Your question is not complete.

According to what do we validate with the equation.

add more info in the question because all of them can be true without any condition given or validation.

7 0

3 years ago

Dante's Mom wants to build a fence around their yard. Here are the measurements of the yard. What are the measurements of the mi

timama [110]

Answer:

(a)The missing measurements are 9 feet and $16\frac{1}{4}$ feet$ .

(b)Therefore, the length of the fence is $97\frac{1}{2}$ feet$

Step-by-step explanation:

The diagram of the yard is attached below.

(a)I have labeled the missing dimensions of the yard as x and y.

Therefore:

$y+8\frac{1}{4}=17 \frac{1}{4}\\y=17 \frac{1}{4}-8\frac{1}{4}\\y=9$ feet$

Similarly:

$x+15\frac{1}{4}=31\frac{1}{2}\\x=31\frac{1}{2}-15\frac{1}{4}\\x=31-15+\frac{1}{2}-\frac{1}{4}\\x=16+\frac{1}{4}\\x=16\frac{1}{4}$ feet$

The missing measurements are 9 feet and $16\frac{1}{4}$ feet$ .

(b)Length of the Fence

The fence is rectangular shaped with:

Length = $31\frac{1}{2}$ feet$

Width = $17 \frac{1}{4}$ feet$

Perimeter of a Rectangle = 2(L+W)

Therefore, the length of the fence

$=2(31\frac{1}{2}+17 \frac{1}{4})\\=2(31+17+\frac{1}{2}+ \frac{1}{4})\\=2(48+ \frac{3}{4})\\=96+\frac{3}{2}\\=97\frac{1}{2}$ feet$

8 0

3 years ago

31.693 Rounded to the nearest Hundredth

ioda

Hi there!

»»————-　★　————-««

I believe your answer is:

31.69

»»————-　★　————-««

Here’s why:

⸻⸻⸻⸻

'9' is in the hundredths place. The rounding is the digit to it's right, or '3'.
Since 3 is less than or equal to 4, we would round down.

⸻⸻⸻⸻

31.693 ≈ 31.69

⸻⸻⸻⸻

»»————-　★　————-««

Hope this helps you. I apologize if it’s incorrect.

7 0

2 years ago

Your patience while we update our system.

Masja [62]

Answer:

equation: 320+x=360, answer: 40

Step-by-step explanation:

add 100,200 and 100 to get 320

360-320=40

x=40

8 0

3 years ago

Write the equation of the line given the slope and a point through the line passes

Anuta_ua [19.1K]

Answer:

1.) Y = 5/3 X + 4

2.) Y = 9/4 X - 27/4

Step-by-step explanation:

Given the slope and the coordinate, linear equation of a line can be expressed by using general linear equation. Which is

Y = MX + C

Where the

Slope M = 5/3

Coordinate = (-3,-1) in which

X = -3, Y = -1

Substitute X, Y and M into the general linear equation to achieve C

-1 = 5/3(-3) + C

-1 = - 5 + C

C = 5 - 1

C = 4

Substitute C and M back into the general linear equation.

Therefore, the equation of the line given the slope and a point through the line passes 5/3, and (-3,-1) to be

Y = 5/3 X + 4

2.) Also,

Slope M = 9/4

Coordinate = (3,0) where X = 3, Y = 0

Substitute X, Y and M into the general linear equation to obtain C

0 = 9/4 (3) + C

C = - 27/4

Substitutes C and M back into the general linear equation

Therefore, the equation of the line given the slope and a point through the line passes 9/4 and (3,0)

Y = 9/4 X - 27/4

4 0

3 years ago