-3(ax^(2)-2y^(2))=-21x^(2)+6y^(2) In the given equation, a is a constant. What is the value of a ?

Distribute -3: We are given the equation -3(ax^(2)-2y^(2))=-21x^(2)+6y^(2). To find the value of a, we need to simplify and compare the coefficients of like terms on both sides of the equation.Simplify equation: First, distribute the -3 on the left side of the equation to both terms inside the parentheses. -3(ax^(2)) + 3(2y^(2)) = -21x^(2) + 6y^(2) This simplifies to -3ax^(2) + 6y^(2) = -21x^(2) + 6y^(2).Compare x^2 coefficients: Now, compare the coefficients of x^(2) on both sides of the equation. On the left side, we have -3a, and on the right side, we have -21. So, -3a = -21.Divide by -3: To find the value of a, divide both sides of the equation by -3. a = (-21) / (-3).Find value of a: Perform the division to find the value of a. a = 7.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

-3(ax^(2)-2y^(2))=-21x^(2)+6y^(2)
In the given equation,
a is a constant. What is the value of
a ?

$-3\left(a x^{2}-2 y^{2}\right)=-21 x^{2}+6 y^{2}$ $\newline$ In the given equation, $a$ is a constant. What is the value of $a$ ?

View step-by-step help

Home

Math Problems

Algebra 2

Find trigonometric ratios using multiple identities

Full solution

-3\left(a x^{2}-2 y^{2}\right)=-21 x^{2}+6 y^{2}

\newline

In the given equation,

a

is a constant. What is the value of

a

Distribute $-3$ : We are given the equation $-3(a x^{2}-2 y^{2})=-21 x^{2}+6 y^{2}$ . To find the value of $a$ , we need to simplify and compare the coefficients of like terms on both sides of the equation.
Simplify equation: First, distribute the $-3$ on the left side of the equation to both terms inside the parentheses. $\newline$ $-3(ax^{2}) + 3(2y^{2}) = -21x^{2} + 6y^{2}$ $\newline$ This simplifies to $-3ax^{2} + 6y^{2} = -21x^{2} + 6y^{2}$ .
Compare $x^2$ coefficients: Now, compare the coefficients of $x^2$ on both sides of the equation. On the left side, we have $-3a$ , and on the right side, we have $-21$ . $\newline$ So, $-3a = -21$ .
Divide by $-3$ : To find the value of $a$ , divide both sides of the equation by $-3$ . $\newline$ $a = \frac{-21}{-3}$ .
Find value of a: Perform the division to find the value of $a$ . $\newline$ $a = 7$ .