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 ?

Question

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 ?

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Set Equations Equal: Given the system of equations: 1) y = 6x - 30 2) y = x^2 - 18x + 114 To find the value of b, we need to solve the system of equations. We can do this by setting the two expressions for y equal to each other and solving for x.Move Terms to Solve: Set the two equations equal to each other: 6x - 30 = x^2 - 18x + 114 Now, we will move all terms to one side to solve for x.Rearrange and Combine: Rearrange the equation: x^2 - 18x + 114 - 6x + 30 = 0 Combine like terms: x^2 - 24x + 144 = 0 This is a quadratic equation in standard form.Factor Quadratic Equation: Factor the quadratic equation: (x - 12)(x - 12) = 0 This gives us a repeated root, meaning x has one value where the equation is true.Solve for x: Solve for x: x - 12 = 0 x = 12 We have found the value of x that satisfies both equations.Substitute x into Equation: Now that we have the value of x, we can substitute it back into either of the original equations to find the value of y, which corresponds to b in the solution (a,b). Let's substitute x into the first equation: y = 6x - 30Calculate Value of y: Substitute x = 12 into the equation: y = 6(12) - 30 Calculate the value of y: y = 72 - 30 y = 42 We have found the value of y, which is the value of b in the solution (a,b).

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

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yamp;=6x−30yamp;=x2−18x+114\begin{align*} y &amp;= 6x-30 \\ y &amp;= x^{2}-18x+114 \end{align*}yy​amp;=6x−30amp;=x2−18x+114​ \newline If (a,b)(a,b)(a,b) is the solution to the system of equations shown, what is the value of bbb? \newline□\square□

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