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${:[y=6x-30],[y=x^(2)-18 x+114]:} If (a,b) is the solution to the system of equations shown, what is the value of b ?$

$y=6 x-30$ $\newline$ $y=x^{2}-18 x+114$ $\newline$ If $(a, b)$ is the solution to the system of equations shown, what is the value of $b$ ?

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Powers with decimal and fractional bases

Full solution

Q.

y=6 x-30

\newline

y=x^{2}-18 x+114

\newline

If

(a, b)

is the solution to the system of equations shown, what is the value of

b

?

Write Equations: Write down the system of equations. $\newline$ We have the following system of equations: $\newline$ $y = 6x - 30$ $\newline$ $y = x^2 - 18x + 114$
Set Equal: Set the two equations equal to each other to find the $x$ -coordinate of the intersection point(s). $6x - 30 = x^2 - 18x + 114$
Rearrange & Solve: Rearrange the equation to set it to zero and solve for $x$ . $x^2 - 18x + 114 - 6x + 30 = 0$ $x^2 - 24x + 144 = 0$
Factor Quadratic: Factor the quadratic equation. $\newline$ $(x - 12)^2 = 0$
Solve for x: Solve for x. $\newline$ $x - 12 = 0$ $\newline$ $x = 12$
Substitute & Find y: Substitute the value of $x$ into one of the original equations to find the value of $y$ . $\newline$ $y = 6x - 30$ $\newline$ $y = 6(12) - 30$ $\newline$ $y = 72 - 30$ $\newline$ $y = 42$

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