Question

How do you solve the equation for $y$ in $7x - 3y = 4$?

Answer 1

Here in this given equation is a linear equation with two variables. Here we have to solve for one variable. To solve this equation for y by using arithmetic operation we can shift the $x$ variable to the right-hand side of the equation then solve the equation for y and on further simplification we get the required solution for the above equation.
The Slope Intercept Form of a Line:
The equation of a line with slope $m$ and making an intercept $c$ on $y$-axis is $y = mx + c$.

Complete step-by-step solution:
Given: $7x - 3y = 4$
We need to transpose ‘$7x$’ to the right-hand side of the equation by subtracting $7x$ on the right-hand side of the equation.
$\Rightarrow - 3y = 4 - 7x$
Now, divide both sides of the equation by $- 3$.
$\Rightarrow y = \dfrac{{4 - 7x}}{{ - 3}}$
$\Rightarrow y = - \dfrac{4}{3} + \dfrac{7}{3}x$
This is the required solution.
If we observe the obtained solution, we notice that it is in the form of the equation slope intercept form. That is $y = mx + c$, where ‘$m$’ is slope and ‘$c$’ is $y$-intercept.
It is in the exact slope intercept form no need to rearrange the equation,
$y = - \dfrac{4}{3} + \dfrac{7}{3}x$, where slope is $- \dfrac{4}{3}$ and the intercept is $\dfrac{7}{3}$.
$y = - \dfrac{4}{3} + \dfrac{7}{3}x$ is the required solution of the given equation.

Note: By putting different values of $x$ and then solving the equation, we can find the values of $y$. The algebraic equation or an expression is a combination of variables and constants, it also contains the coefficient. Generally, we denote the variables with the alphabets. Here both ‘$x$’ and ‘$y$’ are variables. The numerals are known as constants and here $4$ is constant. The numeral of a variable is known as co-efficient and here $7$ is coefficient of ‘$x$’.