If 14y^(2)-21 x=a(2y^(2)-3x), where a is a constant, what is the value of a ?

Given equation: We are given the equation 14y^2 - 21x = a(2y^2 - 3x). To find the value of a, we need to compare the coefficients of corresponding terms on both sides of the equation.Comparing y^2 terms: First, let's compare the coefficients of the y^2 terms. On the left side, the coefficient of y^2 is 14. On the right side, the coefficient of y^2 is 2a. So we have 14 = 2a.Solving for a: Now, let's solve for a by dividing both sides of the equation by 2. 14 / 2 = 2a / 2 7 = aVerifying with x terms: Next, we should verify our result by comparing the coefficients of the x terms. On the left side, the coefficient of x is -21. On the right side, the coefficient of x is -3a. So we have -21 = -3a.Final value of a: Now, let's solve for a by dividing both sides of the equation by -3. -21 / -3 = -3a / -3 7 = aSince we found the same value for a when comparing both the y^2 and x terms, we can conclude that the value of a is indeed 7.

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If
14y^(2)-21 x=a(2y^(2)-3x), where
a is a constant, what is the value of
a ?

If $14 y^{2}-21 x=a\left(2 y^{2}-3 x\right)$ , where $a$ is a constant, what is the value of $a$ ?

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Algebra 2

Composition of linear and quadratic functions: find a value

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Q. If

14 y^{2}-21 x=a\left(2 y^{2}-3 x\right)

, where

a

is a constant, what is the value of

a

Given equation: We are given the equation $14y^2 - 21x = a(2y^2 - 3x)$ . To find the value of $a$ , we need to compare the coefficients of corresponding terms on both sides of the equation.
Comparing $y^2$ terms: First, let's compare the coefficients of the $y^2$ terms. On the left side, the coefficient of $y^2$ is $14$ . On the right side, the coefficient of $y^2$ is $2a$ . $\newline$ So we have $14 = 2a$ .
Solving for a: Now, let's solve for a by dividing both sides of the equation by $2$ . $\newline$ $\frac{14}{2} = \frac{2a}{2}$ $\newline$ $7 = a$
Verifying with $x$ terms: Next, we should verify our result by comparing the coefficients of the $x$ terms. On the left side, the coefficient of $x$ is $-21$ . On the right side, the coefficient of $x$ is $-3a$ . $\newline$ So we have $-21 = -3a$ .
Final value of a: Now, let's solve for a by dividing both sides of the equation by \(-3＂). $\newline$ \(-21 / $-3$ = $-3$ a / $-3$ ＂) $\newline$ \(7 = a＂)
Final value of a: Now, let's solve for a by dividing both sides of the equation by $-3$ . $\newline$ $-21 / -3 = -3a / -3$ $\newline$ $7 = a$ Since we found the same value for a when comparing both the $y^2$ and $x$ terms, we can conclude that the value of a is indeed $7$ .