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Anuta_ua [19.1K]
2 years ago
6

Solve the system of equations algebraically. 5g+4k=10 -3g-5k=7

Mathematics
2 answers:
Alisiya [41]2 years ago
8 0

Answer:

k = -5

g = 6

Step-by-step explanation

1) First solve for k and plug that into the other equation to solve for g.

5g + 4k = 10

4k = -5g + 10

k = -5/4g + 2.5

2) Plug k into the other equation to solve for g

-3g - 5k = 7

-3g = 5k + 7

-3g = 5(-5/4g + 2.5) + 7         Use the distributive property

-3g = -6.25g + 12.5 + 7        Combine like terms and simplify

-3g = -6.25g + 19.5               Add 6.25g to both sides

3.25g = 19.5                          Divide 3.25 from both sides to find g

g = 6

3) Now we take this g and plug it into the other equation to find k

(we could also just plug it into this equation as well)

5g + 4k = 10

5(6) + 4k = 10

30 + 4k = 10

4k = -20

k = -5.

If we really wanted to doube check this then we could plug the k value into the equation we used to find the g value...

-3(6) - 5(-5) = 7

-18 + 25 = 7

So yes, k = -5 and g = 6.

andreev551 [17]2 years ago
7 0
You want to find a common value which will be 15g
3(5g+4k=10)
5(-3g-5k=7)

15g+12k=30
-15g-25k=35
cross out the g and add the rest
-13k=36
k=-5
Then substitute -5 as k into the original equation
5g+4(-5)=10
5g-20=10
5g=30
g=6
So, K=-5 and G=6
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Brrunno [24]

Answers:

bio = 258

sociology = 169

============================================================

Work Shown:

x = number of bio textbooks

y = number of sociology textbooks

x+y = 427 books sold total

y = x-89 since 89 less sociology textbooks were sold compared to bio

Apply substitution to get the following

x+y = 427

x+x-89 = 427 ... replace y with x-89

2x-89 = 427

2x = 427+89

2x = 516

x = 516/2

x = 258 bio textbooks were sold

y = x-89

y = 258-89

y = 169 sociology textbooks were sold

5 0
1 year ago
Find midpoint (-6, 3) (4,-3)
Crank
<h2>Coordinate of mid point = (1,0)</h2>

Step-by-step explanation:

Given points are (-6,3) and (4,-3)

x_1=-6 ,    y_1=3 ,  x_2= 4    and  y_2 = -3

Coordinate of mid point (\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )

                                     =(\frac{-6+4}{2} ,\frac{3+(-3)}{2})

                                      =(1,0)

5 0
3 years ago
Heron Island is a coral cay in the Great Barrier Reef. Around Heron Island (and elsewhere in Australia) there are 2 color morphs
kobusy [5.1K]

In case A, as the error would be a difference of 1, the assumption could be mantained, but in case B the difference will be bigger, showing that the ratio is not 3:1 but 4:1.

<h3><u>Ratios</u></h3>

Given that a preliminary study was carried out to test the hypothesis that the ratio of white to dark herons on the island was 3:1, but A) a small census found 16 white morphs and 4 dark, to determine if the assumption of a 3 :1 ratio could be rejected, and B) to determine the same question if the census were larger with 160 white morphs and 40 dark, the following calculations must be made:

A)

  • 3 + 1 = 4
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  • 4 = 20
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  • 60 / 4 = X
  • 15 = X
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B)

  • 3 + 1 = 4
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Learn more about ratios in brainly.com/question/1504221

3 0
2 years ago
Explain how 9 x 4 can help you find 9 x 8
MrMuchimi
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Read 2 more answers
Given the equation y − 3 = 1/2 (x + 6) in point-slope form, identify the equation of the same line in standard form. )
Doss [256]

Answer:

a: x − 2y = −12

Step-by-step explanation:

the standard form of a line is is usually given as Ax + By = C, so just by deduction you can tell that the correct answer is a.

If you want to do the procedure it would be:

y − 3 = 1/2 (x + 6)

y − 3 = 1/2 x + 3

y - 1/2 x = 3 + 3

y - 1/2 x = 6

(y - 1/2 x = 6) * 2 to get rid of the fraction

2y - x = 12  rearrenge the terms

x - 2y = -12

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