The relationship between two numbers is described below, where x represents the first number and y represents the second number. The square of the first number is equal to the sum of the second number and 16. The difference of 4 times the second number and 1 is equal to the first number multiplied by 7. Select the equations that form the system that models this situation. Then, select the solution (s) of the system. Equations Solutions y2 + 16 = x (2x) 2 = y + 16 (1,15) (5,9) x2 = y + 16 7y - 1 = 4x (2,-12) (8,48) 1 - 4y = 7x 4y - 1 = 7x (4,-7) (9,3) NextReset

Question

Andrew Chen

Mathematics

6 January, 22:30

The relationship between two numbers is described below, where x represents the first number and y represents the second number. The square of the first number is equal to the sum of the second number and 16. The difference of 4 times the second number and 1 is equal to the first number multiplied by 7. Select the equations that form the system that models this situation. Then, select the solution (s) of the system. Equations Solutions y2 + 16 = x (2x) 2 = y + 16 (1,15) (5,9) x2 = y + 16 7y - 1 = 4x (2,-12) (8,48) 1 - 4y = 7x 4y - 1 = 7x (4,-7) (9,3) NextReset

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Jaydon Herring · Answer 1

The first number is x and the second number is y;

x^2=y+16

y=x^2-16 ... i

4y-1=7x ... ii

factoring i we get:

y = (x-4) (x+4)

therefore:

x^2-16 = (7x+1) / 4

4 (x^2-16) = 7x+1

4x^2-64=7x+1

this will be:

4x^2-7x-65=0

solving the above we get:

x=-13/4 or x=5

when x=5

x^2=y+16

5^2=y+16

y=5^2-16

y=25-16

y=9

therefore the answer is:

The equations are:

x^2=y+16

4y-1=7x

(5,9)