Question

How do you solve for y in $4x + 7y = 28$ ?

Answer 1

Here in this given equation is a linear equation. 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 RHS then solve the equation for y and on further simplification we get the required solution for the above equation.

Complete step-by-step solution:
The given equation is a linear equation. These equations are defined for lines in the coordinate system. An equation for a straight line is called a linear equation. The general representation of the straight-line equation is $y = mx + b$, it involves only a constant term and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, this equation is called a "linear equation of two variables," where y and x are the variables.
Consider the given equation
$\Rightarrow \,\,\,\,4x + 7y = 28$
We have to shift the variable x and its coefficient to the RHS, by add -4x on both sides, then
$\Rightarrow \,\,\,\,4x + 7y - 4x = 28 - 4x$
On simplification we get
$\Rightarrow \,\,\,\,7y = 28 - 4x$
To solve the equation for y, divide 7 by both sides, then
$\Rightarrow \,\,\,\,\dfrac{{7y}}{7} = \dfrac{{28 - 4x}}{7}$
$\Rightarrow \,\,\,\,y = \dfrac{{28}}{7} - \dfrac{4}{7}x$
$\Rightarrow \,\,\,\,y = 4 - \dfrac{4}{7}x$
Hence, the y value of the given linear equation $4x + 7y = 28$ is $y = \dfrac{5}{2} - \dfrac{7}{2}x$.

Note: The algebraic equation or an expression is a combination of variables and constants, it also contains the coefficient. The alphabets are known as variables. The x, y, z etc., are called as variables. The numerals are known as constants. The numeral of a variable is known as co-efficient. We have 3 types of algebraic expressions namely monomial expression, binomial expression and polynomial expression. By using the tables of multiplication, we can solve the equation.