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${:[y=(x-5)^(2)+1],[(y-5)/(3)=15]:} If (x,y) is a solution to the system of equations shown and x > 0, what is the value of x ?$

$y=(x-5)^{2}+1$ $\newline$ $\frac{y-5}{3}=15$ $\newline$ If $(x, y)$ is a solution to the system of equations shown and x>0 , what is the value of $x$ ?

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Evaluate exponential functions

Full solution

Q.

y=(x-5)^{2}+1

\newline

\frac{y-5}{3}=15

\newline

If

(x, y)

is a solution to the system of equations shown and

x>0

, what is the value of

x

?

Solve Second Equation for y: We have the system of equations: $\newline$ $1$ ) $y = (x - 5)^2 + 1$ $\newline$ $2$ ) $(y - 5)/3 = 15$ $\newline$ First, we will solve the second equation for $y$ .
Find y Value: Solve the second equation $(y - 5)/3 = 15$ for y. $\newline$ Multiply both sides by $3$ to isolate $y - 5$ . $\newline$ $(y - 5) = 15 \times 3$ $\newline$ $y - 5 = 45$ $\newline$ Now, add $5$ to both sides to find y. $\newline$ $y = 45 + 5$ $\newline$ $y = 50$ $\newline$ We have found the value of y.
Substitute $y$ into First Equation: Now that we have $y = 50$ , we can substitute this value into the first equation $y = (x - 5)^2 + 1$ to find $x$ . Substitute $y$ with $50$ in the first equation. $50 = (x - 5)^2 + 1$
Solve for x: Next, we will solve for $x$ . $\newline$ Subtract $1$ from both sides of the equation to isolate the squared term. $\newline$ $50 - 1 = (x - 5)^2$ $\newline$ $49 = (x - 5)^2$ $\newline$ Now, take the square root of both sides to solve for $x - 5$ . $\newline$ $\sqrt{49} = x - 5$ $\newline$ $\pm7 = x - 5$ $\newline$ Since we are given that x > 0, we will only consider the positive root.
Find x Value: Add $5$ to both sides of the equation to solve for $x$ . $\newline$ $7 + 5 = x$ $\newline$ $x = 12$ $\newline$ We have found the value of $x$ .

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