Solveeit Logo
Login

Question

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

How do you solve for y in −9x−7=2y+7 - 9x - 7 = 2y + 7 ?

Explanation

Solution

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+by = 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
⇒    −9x−7=2y+7\Rightarrow \,\,\,\, - 9x - 7 = 2y + 7
Rearrange the equation because we have to shift the variable x and its coefficient to the RHS.
⇒    2y+7=−9x−7\Rightarrow \,\,\,\,2y + 7 = - 9x - 7
Subtract both side by 7, then
⇒    2y+7−7=−9x−7−7\Rightarrow \,\,\,\,2y + 7 - 7 = - 9x - 7 - 7
On simplification we get
⇒    2y=−9x−14\Rightarrow \,\,\,\,2y = - 9x - 14
To solve the equation for y, divide 2 by both sides, then
⇒    2y2=−9x−142\Rightarrow \,\,\,\,\dfrac{{2y}}{2} = \dfrac{{ - 9x - 14}}{2}
⇒    y=−9x2−142\Rightarrow \,\,\,\,y = - \dfrac{{9x}}{2} - \dfrac{{14}}{2}
⇒    y=−9x2−7\Rightarrow \,\,\,\,y = - \dfrac{{9x}}{2} - 7
Hence, the y value of the given linear equation −9x−7=2y+7 - 9x - 7 = 2y + 7 is y=−9x2−7y = - \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.