Question

Find the solution of \[9y - 4\left( {y + 5} \right) = 40\].

Answer 1

Hint:Linear equations are the equations in which the variables are raised to the power equal to one. The best way to solve a linear equation in one variable is to rearrange the linear equation in such a way that we could write all the variable terms to the left hand side of the equation. The linear equations are classified into different types based on the number of variables in the equation. Linear equations are the equations in which the variables are raised to the power equal to one.

Complete step by step answer:
This equation has one variable “y” also called an unknown. Solving this equation means to find all the real values that “y” can assume.
Here are the steps that we can follow to get the value of “y”.
First we need to expand the brackets,
This means that we multiply the number outside the brackets by every term that's in the brackets.
So, \[ - 4\left( {y + 5} \right)\]becomes\[ - 4 \times y + \left( { - 4} \right) \times 5 = - 4y - 20\].
\[ \Rightarrow 5y - 20 = 40\]
This is obtained by putting the expansion in\[9y - 4\left( {y + 5} \right) = 40\].
Now we can have the above equation as,
\[5y - 20 = 40 \\
\Rightarrow 5y = 40 + 20 \\
\Rightarrow 5y = 60 \\
\Rightarrow y = \dfrac{{60}}{5} \\
\therefore y = 12 \\ \]
Hence the solution of \[9y - 4\left( {y + 5} \right) = 40\] is \[12\].

Note:Linear equations graphically always represent a straight line. Linear equations in one variable give a line parallel to coordinate axes. Linear equation is the equation with degree one. It does not have anything to do with the number of variables in the equation. A linear equation can have two, three or more variables in it as long as the degree of the equation is equal to one.