Question

How do you solve $ 2y - 10 + 18y = 10y - 3 \times 30? $

Answer 1

Hint: As we know that the above given equation is a linear equation. An equation for a straight line is called a linear equation. The standard form of linear equations in two variables is $ Ax + By = C $ . When an equation is given in this form it’s also pretty easy to find both intercepts $ (x,y) $ . By transferring the positive $ a $ to the right hand side value gives the required solution.

Complete step by step solution:
As we know that the above given equation is a linear equation and to solve for $ y $ we need to isolate the term containing $ y $ on the left hand side i.e. to simplify
 $ 2y - 10 + 18y = 10y - 3 \times 30 $
 and move all the terms to the right.
First we will multiply the value in the right hand side of the equation:
 $ 2y - 10 + 18y = 10y - 90 $ .
Now moving all the terms containing $ y $ to the left hand side:
 $ 2y + 18y - 10y = 10 - 90 $ .
We will solve it now,
 $ 10y = - 80 $ .
It gives, $ y = \dfrac{{ - 80}}{{10}} $ .
Hence the answer of $ 2y - 10 + 18y = 10y - 3 \times 30 $ is $ y = - 8 $ .
So, the correct answer is “ $ y = - 8 $ ”.

Note: We should keep in mind the positive and negative signs while calculating the value of any variable as it will change it’s slope and value. In the equation $ Ax + By = C $ , $ A $ and $ B $ are real numbers and $ C $ is a constant, it can be equal to zero $ (0) $ also. These types of equations are of first order. Linear equations are also first-degree equations as it has the highest exponent of variables as $ 1 $ . The slope intercept form of a linear equation is $ y = mx + c $ ,where $ m $ is the slope of the line and $ b $ in the equation is the y-intercept and $ x $ and $ y $ are the coordinates of x-axis and y-axis , respectively.