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8y=4x^(2)-12 x+46

y=(3)/(2)x+(5)/(4)
If
(a,b) is the solution to the system of equations shown, what is the value of
a ?

$8 y=4 x^{2}-12 x+46$ $\newline$ $y=\frac{3}{2} x+\frac{5}{4}$ $\newline$ If $(a, b)$ is the solution to the system of equations shown, what is the value of $a$ ?

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Evaluate recursive formulas for sequences

Full solution

Q.

8 y=4 x^{2}-12 x+46

\newline

y=\frac{3}{2} x+\frac{5}{4}

\newline

If

(a, b)

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

a

?

Substitute $y$ into first equation: We have a system of two equations: $\newline$ $1$ ) $8y = 4x^2 - 12x + 46$ $\newline$ $2$ ) $y = \frac{3}{2}x + \frac{5}{4}$ $\newline$ To find the solution to the system, we need to substitute the second equation into the first one to solve for $x$ .
Distribute $8$ on left side: Substitute $y$ from the second equation into the first equation: $\newline$ $8\left(\frac{3}{2}x + \frac{5}{4}\right) = 4x^2 - 12x + 46$
Rearrange equation and solve: Distribute $8$ on the left side of the equation: $\newline$ $8 \times \left(\frac{3}{2}\right)x + 8 \times \left(\frac{5}{4}\right) = 4x^2 - 12x + 46$ $\newline$ $12x + 10 = 4x^2 - 12x + 46$
Divide and simplify: Rearrange the equation to set it to zero and solve for $x$ : $4x^2 - 12x - 12x - 10 + 46 = 0$ $4x^2 - 24x + 36 = 0$
Factor the quadratic equation: Divide the entire equation by $4$ to simplify: $\newline$ $x^2 - 6x + 9 = 0$
Set factors equal to zero: Factor the quadratic equation: $\newline$ (x - \(3)(x - $3$ ) = $0$
Find $x$ value: Set each factor equal to zero and solve for $x$ : $x - 3 = 0$ $x = 3$
Final solution for $a$ : We found the value of $x$ to be $3$ . Since we are looking for the value of $a$ , and $(a,b)$ is the solution to the system, $a = x$ .

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