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$4y^2+9=6x+3$ and $4y=2x+1$ If $x$ is the solution to the system of equations shown, what is the value of $y$ ?

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Solve linear equations: mixed review

Full solution

Q.

4y^2+9=6x+3

and

4y=2x+1

If

x

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

y

?

Write Equations: First, let's write down the system of equations we need to solve: $\newline$ $1$ . $4y^2 + 9 = 6x + 3$ $\newline$ $2$ . $4y = 2x + 1$ $\newline$ We need to find the value of $y$ when $x$ is the solution to these equations.
Solve for y: Let's solve the second equation for y to get $y$ in terms of $x$ . $4y = 2x + 1$ Divide both sides by $4$ to isolate $y$ : $y = \frac{2x + 1}{4}$
Substitute $y$ into first equation: Now we will substitute the expression for $y$ from the second equation into the first equation. $\newline$ Replace $y$ in the first equation with $(2x + 1) / 4$ : $\newline$ $4((2x + 1) / 4)^2 + 9 = 6x + 3$
Simplify equation: Simplify the equation by squaring the term $(2x + 1) / 4$ and multiplying by $4$ : $(2x + 1)^2 / 4 + 9 = 6x + 3$ $(4x^2 + 4x + 1) / 4 + 9 = 6x + 3$
Eliminate fraction: Multiply through by $4$ to eliminate the fraction: $4x^2 + 4x + 1 + 36 = 24x + 12$
Combine like terms: Combine like terms: $4x^2 + 4x + 37 = 24x + 12$
Create quadratic equation: Subtract $24x$ and $12$ from both sides to get a quadratic equation: $\newline$ $4x^2 - 20x + 25 = 0$
Check for mistakes: This quadratic equation does not match the original system of equations after substitution. There seems to be a mistake in the previous steps. We need to go back and check our calculations.

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