Question

How do you solve $3x+7y=21$ for y?

Answer 1

Hint: We need to solve this equation in terms of x. As it is given to us a normal equation, therefore we try to make the value of y in terms of x. So, we start solving this problem. We will subtract 3x on both sides of the equation. Then we know, the same terms with opposite signs cancel out, thus we get a new equation, and then divide both sides of the new equation by 7. After the necessary calculation, we split the denominator on the right-hand side of the equation with respect to subtraction and make needful calculations to get the value of y in terms of x.

Complete step by step answer:
According to the question, it is given to a normal equation. We have to solve this equation for y and get the value in terms of x.
The equation is given to us: $3x+7y=21$ ------------- (1)
Firstly, we will subtract $3x$ on both sides in the equation (1), we get
$\Rightarrow 3x+7y-3x=21-3x$
As we know, the same terms with opposite signs cancel out, therefore we get
$\Rightarrow 7y=21-3x$
Now, we will divide 7 on both sides of the above equation, we get
$\Rightarrow \dfrac{7y}{7}=\dfrac{21-3x}{7}$
We know in the division, the same terms will cancel out to 1, thus on the left-hand side we apply the division rule, we get
$\Rightarrow y=\dfrac{21-3x}{7}$
Now, we will split the denominator with respect to subtraction on the right-hand side of the above equation, we get
$\Rightarrow y=\dfrac{21}{7}-\dfrac{3x}{7}$
After necessary calculations, we get
$\Rightarrow y=3-\dfrac{3}{7}x$

Therefore, we see that for the equation $3x+7y=21$ value of y is equal to $3-\dfrac{3}{7}x$ that is in terms of x, which is the required answer.

Note: Make all the necessary calculations and do a step-by-step calculation, to avoid errors. In this question, we have to solve for y, thus we get the value of y in terms of x. Now, if you substitute any value of x in the required answer, you will get an integer value as your value of y.