Question

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Explanation:

Step1: Translate first condition to equation

The square of the first number ($x^2$) equals the sum of the second number ($y$) and 16:
$x^2 = y + 16$

Step2: Translate second condition to equation

4 times the second number minus 1 equals 7 times the first number:
$4y - 1 = 7x$

Step3: Test ordered pairs in equations

Substitute $(9,3)$ into $x^2 = y + 16$:
$9^2 = 3 + 16 \implies 81 = 19$ (False)
Substitute $(8,48)$ into $x^2 = y + 16$:
$8^2 = 48 + 16 \implies 64 = 64$ (True)
Substitute $(8,48)$ into $4y - 1 = 7x$:
$4(48) - 1 = 7(8) \implies 192 - 1 = 56 \implies 191 = 56$ (False)
Substitute $(2,-12)$ into $x^2 = y + 16$:
$2^2 = -12 + 16 \implies 4 = 4$ (True)
Substitute $(2,-12)$ into $4y - 1 = 7x$:
$4(-12) - 1 = 7(2) \implies -48 - 1 = 14 \implies -49 = 14$ (False)
Substitute $(1,15)$ into $x^2 = y + 16$:
$1^2 = 15 + 16 \implies 1 = 31$ (False)
Substitute $(4,-7)$ into $x^2 = y + 16$:
$4^2 = -7 + 16 \implies 16 = 9$ (False)
Substitute $(5,9)$ into $x^2 = y + 16$:
$5^2 = 9 + 16 \implies 25 = 25$ (True)
Substitute $(5,9)$ into $4y - 1 = 7x$:
$4(9) - 1 = 7(5) \implies 36 - 1 = 35 \implies 35 = 35$ (True)

Answer:

Equations: $x^2 = y + 16$, $4y - 1 = 7x$
Solution ordered pair: $(5,9)$