Question

How do you solve for y in \[7x + 2y = 5\] ?

Answer 1

Hint: 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
\[ \Rightarrow \,\,\,\,7x + 2y = 5\]
We have to shift the variable x and its coefficient to the RHS, by add -7x on both sides, then
\[ \Rightarrow \,\,\,\,7x + 2y - 7x = 5 - 7x\]
On simplification we get
\[ \Rightarrow \,\,\,\,2y = 5 - 7x\]
To solve the equation for y, divide 2 by both sides, then
\[ \Rightarrow \,\,\,\,\dfrac{{2y}}{2} = \dfrac{{5 - 7x}}{2}\]
\[ \Rightarrow \,\,\,\,y = \dfrac{5}{2} - \dfrac{7}{2}x\]
Hence, the y value of the given linear equation \[7x + 2y = 5\] 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.