Question

Solve: $ 3(y - 3) = 5(2y + 1) $

Answer 1

Hint: As we know that the above given equation $ 3a + 2b = c $ 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) $ . In this question we will multiply the polynomial and then solve it.

Complete step-by-step answer:
As we know that the above given equation is a linear equation and to solve for $ y $ . So we need to isolate the term containing $ y $ on the left hand side i.e. to simplify $ 3(y - 3) = 5(2y + 1) $ .
 Here on multiplying we will get $ 3 \times y - 3 \times 3 = 5 \times 2y + 5 \times 1 \Rightarrow 3y - 9 = 10y + 5 $ and then by transferring the similar terms together we have $ 3y - 10y = 9 + 5 \Rightarrow - 7y = 14 $
It gives, $ y = \dfrac{{14}}{{ - 7}} = - 2 $ .
Hence the required value of the linear equation is $ y = - 2 $ .
So, the correct answer is “ $ y = - 2 $ ”.

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.