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Leya [2.2K]
3 years ago
12

Which is the solution to the system 3x+y=8 and 7x−4y=25

Mathematics
1 answer:
tatyana61 [14]3 years ago
7 0

Answer:

(3, - 1 )

Step-by-step explanation:

Given the 2 equations

3x + y = 8 → (1)

7x - 4y = 25 → (2)

Multiplying (1) by 4 and adding to (2) will eliminate the y- term

12x + 4y = 32 → (3)

Add (2) and (3)  term by term to eliminate y

19x + 0 = 57

19x = 57 ( divide both sides by 19 )

x = 3

Substitute x = 3 into either of the 2 equations and solve for y

Substituting into (1)

3(3) + y = 8

9 + y = 8 ( subtract 9 from both sides )

y = - 1

solution is (3, - 1 )

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Option d is the correct answer. $38,430.00 is the amount saved for a down payment given that Mr. and Mrs. Lorenzo want to buy a home valued at $213,500 and they have 18% of this amount saved for the down payment. This can be obtained by using percentage formula.

<h3>How much have they saved?</h3>

The percentage of a number can be obtained using percentage formula,

If P% of X is Y then it can be denoted using the formula of percentage as,

⇒ P% of X = Y

⇒ P% × X = Y   (where P% is P/100)

Here in the question it is given that,

  • Mr. and Mrs. Lorenzo want to buy a home valued at $213,500
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We have to find the amount they saved for the down payment.

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The amount they saved for the down payment,

18% of the total amount = 18% of $213,500

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18% of $213,500 = 18% × $213,500  

18% of $213,500 = 18/100 × $213,500

18% of $213,500 = $ 38,430.00

Hence Option d is the correct answer. $38,430.00 is the amount saved for a down payment given that Mr. and Mrs. Lorenzo want to buy a home valued at $213,500 and they have 18% of this amount saved for the down payment.

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