This is simple algebra, but i'm lost?

Question

"Find two numbers such that 4 times the first number minus 4 times the second number equals 24 and twice the first number times the second number equals 30'

Easy Ten Points If Answer IS Given

Answer 1

4x - 4y = 24

2xy = 30

Divide the first equation by 4:

x - y = 6

-> y = 6 + x

Divide the second one by 2:

xy = 15

-> x(6+ x) = 15

x^2 + 6x = 15

Complete the square:

x^2 + 6x + 9 = 24

x + 3 = ±sqrt(24) = ±2 sqrt(6)

x = -3 ± 2 sqrt(6)

Answer 2

Let the numbers be A and B

Equation 1:

4A - 4B = 24

Equation 2:

2AB = 30

Simplify the first equation:

4(A - B) = 24

A - B = 24/4

A - B = 6

Solve for A:

A = B + 6

Substitute into equation #2:

2(B + 6) * B = 30

2B(B + 6) = 30

2B² + 12B = 30

Get everything on one side:

2B² + 12B - 30 = 0

Divide both sides by 2:

B² + 6B - 15 = 0

This doesn't factor nicely so you would have to use the quadratic formula:

B = 1.899 or B = -7.899

A = 7.899 or A = -1.899

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