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${:[4y^(2)+9=6x+3],[4y=2x+1]:} If (x,y) is the solution to the system of equations shown, what is the value of y ? ◻$

$\begin{array}{r} 4 y^{2}+9=6 x+3 \\ 4 y=2 x+1 \end{array}$ $\newline$ If $(x, y)$ is the solution to the system of equations shown, what is the value of $y$ ? $\newline$ $\square$

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Quotient property of logarithms

Full solution

Q.

\begin{array}{r} 4 y^{2}+9=6 x+3 \\ 4 y=2 x+1 \end{array}

\newline

If

(x, y)

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

y

?

\newline

\square

Solve for y: First, let's solve the second equation for y. $\newline$ $4y = 2x + 1$ $\newline$ Divide both sides by $4$ to isolate $y$ . $\newline$ $y = \frac{2x + 1}{4}$
Substitute in first equation: Now, substitute $y$ in the first equation with the expression we found. $4\left(\frac{2x + 1}{4}\right)^2 + 9 = 6x + 3$
Simplify by squaring: Simplify the equation by squaring the expression for $y$ . $4\left(\frac{4x^2 + 4x + 1}{16}\right) + 9 = 6x + 3$
Clear the fraction: Multiply through by $4$ to clear the fraction. $(4x^2 + 4x + 1) + 36 = 24x + 12$
Combine like terms: Combine like terms. $4x^2 + 4x + 37 = 24x + 12$
Set equation to zero: Subtract $24x$ and $12$ from both sides to set the equation to zero. $\newline$ $4x^2 - 20x + 25 = 0$

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