Question

How do you solve for y in \[ - 9x - 7 = 2y + 7\] ?

Answer 1

Hint: 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.

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
\[ \Rightarrow \,\,\,\, - 9x - 7 = 2y + 7\]
Rearrange the equation because we have to shift the variable x and its coefficient to the RHS.
\[ \Rightarrow \,\,\,\,2y + 7 = - 9x - 7\]
Subtract both side by 7, then
\[ \Rightarrow \,\,\,\,2y + 7 - 7 = - 9x - 7 - 7\]
On simplification we get
\[ \Rightarrow \,\,\,\,2y = - 9x - 14\]
To solve the equation for y, divide 2 by both sides, then
\[ \Rightarrow \,\,\,\,\dfrac{{2y}}{2} = \dfrac{{ - 9x - 14}}{2}\]
\[ \Rightarrow \,\,\,\,y = - \dfrac{{9x}}{2} - \dfrac{{14}}{2}\]
\[ \Rightarrow \,\,\,\,y = - \dfrac{{9x}}{2} - 7\]
Hence, the y value of the given linear equation \[ - 9x - 7 = 2y + 7\] is \[y = - \dfrac{{9x}}{2} - 7\].

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.