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beks73 [17]
2 years ago
6

Show and explain how replacing one equation by the sum of that equation and a multiple of the other produces a system with the s

ame solutions as the one shown. 8x + 7y = 39 4x – 14y = –68
Mathematics
1 answer:
telo118 [61]2 years ago
3 0

Answer:

(1/2, 5)

Step-by-step explanation:

8x + 7y = 39

-2(4x - 14y = -68)

-8x + 28y = 136

8x + 7y = 39

add the two equations together

35y = 175

y = 5

8x + 7(5) = 39

8x = 4

x = 1/2

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After the booster club sold 40 hotdogs at a football game, it had 90$ in profit. After the next game, it had sold a total of 80
sergiy2304 [10]
Let's first establish what we already know for this problem.

x = total number of hotdogs sold
y = total profit from total sales of hotdogs

Let's also establish the other equations which we will require in order to solve this problem.

Equation No. 1 -
Profit for 40 hotdogs = $90 profit

Equation No. 2 -
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STEP-BY-STEP SOLUTION

From this, we can use the formula y = mx + b & substitute the values for x & y from one of the two previous equations into the formula in order to obtain the values of m & b for the final equation. Here is an example of the working out as displayed below:

Firstly, using the first or second equation, we make either m or b the subject. Here I have used the first equation and made m the subject:

Equation No. 1 -
y = mx + b
90 = m ( 40 ) + b
40m = 90 - b
m = ( 90 - b ) / 40

Now, make b the subject in the second equation as displayed below:

Equation No. 2 -
y = mx + b
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210 = 80m + b
b = 210 - 80m

Then, substitute m from the first equation into the second equation.

Equation No. 2 -
b = 210 - 80m
b = 210 - 80 [ ( 90 - b ) / 40 ]
b = 210 - [ 80 ( 90 - b ) / 40 ]
b = 210 - 2 ( 90 - b )
b = 210 - 180 - 2b
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Now, substitute b from the second equation into the first equation.

Equation No. 1 -
m = ( 90 - b ) / 40
m = ( 90 - ( - 30 ) / 40
m = ( 90 + 30 ) / 40
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Through this, we have established that:

m = 3
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y = mx + b
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ANSWER:
y = 3x - 30
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