Question

How do you solve for y in $4xy + 3 = 5z$ ?

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
$\Rightarrow \,\,\,\,4xy + 3 = 5z$
Subtract 3 on both side
$\Rightarrow \,\,\,\,4xy + 3 - 3 = 5z - 3$
On simplification we get
$\Rightarrow \,\,\,\,4xy = 5z - 3$
To solve the equation for y. We have to shift the variable x and its coefficient to the RHS, by divide 4x on both side
$\Rightarrow \,\,\,\,\dfrac{{4xy}}{{4x}} = \dfrac{{5z}}{{4x}} - \dfrac{3}{{4x}}$
On simplification we get
$\Rightarrow \,\,\,\,y = \dfrac{5}{4}\dfrac{z}{x} - \dfrac{3}{4}\dfrac{1}{x}$
Hence, the y value of the given linear equation $4xy + 3 = 5z$ is $y = \dfrac{5}{4}\dfrac{z}{x} - \dfrac{3}{4}\dfrac{1}{x}$.

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.