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DochEvi [55]
3 years ago
9

−4x+7y+5=0 x−3y=−5 ​ How many solutions does the system have?

Mathematics
1 answer:
xeze [42]3 years ago
3 0

   

Solution:  

Using Substitution Method:

-4x+7y=-5   (Equation 1)

x-3y=-5       (Equation 2)

get the value of x from Equation 2

x=3y-5     (Equation 3)  

Put the value of x from Equation 3 in Equation 1

-4(3y-5)+7y=-5

-4(3y)+20+7y=-5

-12y+7y=-5-20

-5y=-25

Negative sign on both sides cancels each other

y=25/5

y=5

Putting value of y in equation 3

x=3(5)-5

x=15-5

x=10

Therefore,   [x,y]=[10,5]

Using Elimination Method

-4x+7y=-5   (Equation 1)

x-3y=-5       (Equation 2)

Multiply equation 2 with -4 in order to eliminate the x term

-4(x-3y)=-5*4

-4x+12y=20     (Equation 3)

Adding Equation 1 and 3

-4x+7y=-5    

-4x+12y=20    

+    -     = -   (Change Of Sign with x and y terms)

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

0x-5y = -25

-5y=-25

y=5  

Substituting y’s value is Equation 1

-4x+7(5)=-5

-4x+35=-5

-4x=-40

Cancellation of negative sign on both sides

x=40/4

x=10

[x,y]=[10,5]

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The number of rows = 80

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total number of seats is the product of the number of rows and number of seats per row = 80*50 = 4000
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Classify the following triangle. Check all that apply.
cluponka [151]

Answer:

Right, obtuse, and isosceles. (B, D, E)

6 0
3 years ago
The perimeter of a playing field for a certain sport is 174 ft. The field is a rectangle, and the length is 45 ft longer than th
Leno4ka [110]

Answer:

21 ft by 66 ft

Step-by-step explanation:

From the question,

P = 2(L+W)............... Equation 1

Where P = Perimeter of the playing Field, L = Length of the playing Field, W = width of the playing Field.

If the Length of the Field is 45 ft longer than the width,

L = 45+W............ Equation 2

Substitute Equation 2 into equation 1

P = 2(45+W+W)

P = 90+4W............. Equation 3

Given: P = 174 ft.

Substitute into equation 3

174 = 90+4W

4W = 174-90

4W = 84

W = 84/4

W = 21 ft.

Substituting the value of W into equation 2

L = 45+21

L = 66 ft.

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3 0
3 years ago
Vanessa uses the expressions (3x² + 5x + 10) and (x² – 3x - 1) to represent the length and width of her patio.
Kay [80]

Answer:

a) 3x⁴-4x³-8x²-35x-10

Step-by-step explanation:

3x2(x²-3x-1)+5x(x²-3x-1)+10(x²-3x-1)

3x⁴-9x³-3x²+5x³-15x²-5x+10x²-30x-10

3x⁴-9x³+5x³-3x²-15x²+10x²-5x-30x-10

3x⁴-4x³-8x²-35x-10

5 0
2 years ago
<img src="https://tex.z-dn.net/?f=g%28x%29%20%3D%203x%20-%206" id="TexFormula1" title="g(x) = 3x - 6" alt="g(x) = 3x - 6" align=
VARVARA [1.3K]

Hey there! :)

Answer:

g^{-1} (g(10))=10

Step-by-step explanation:

Begin by calculating g(10):

g(x) = 3x - 6

Substitute in 10 for x:

g(10) = 3(10) - 6

g(10) = 30-6

g(10) = 24.

Plug '24' into 'x' into g^{-1} (x)

g^{-1} (24)=\frac{(24) + 6}{3}

Simplify:

g^{-1} (24)=\frac{30}{3}

g^{-1} (24)=10

3 0
3 years ago
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