Question

‌How‌ ‌do‌ ‌you‌ ‌solve‌ ‌$3y-4=2y-5$?‌

Answer 1

Hint: The given equation in the above question is a linear equation in terms of the variable $y$. This means that it will have a single solution. For solving the given equation, we have to separate all the variable terms on one the left hand side, and all the constant terms on the right hand side of the equation. For this we need to subtract $2y$ from both sides of the given equation to get all the variable terms on the left hand side. Then we have to add $4$ on both sides to get all the constants on the right hand side. Finally, on simplifying both the sides of the resultant equation, we will get the final solution of the given equation.

Complete step-by-step solution:
The equation given in the above question is written as
$\Rightarrow 3y-4=2y-5$
For solving the above equation, we need to separate all the variables on one side, and all the constants on the other side of the equation. So we subtract $2y$ from both the sides of the above equation to get
$\begin{align}
  & \Rightarrow 3y-4-2y=2y-5-2y \\
 & \Rightarrow y-4=-5 \\
\end{align}$
Now, we add $4$ on both the sides to get
$\begin{align}
  & \Rightarrow y-4+4=-5+4 \\
 & \Rightarrow y=-1 \\
\end{align}$
Hence, we have obtained the solution of the given equation as $y=-1$.

Note: We can also solve the given equation graphically. For this, we need to equate each side of the given equation to the variable $x$ so as to write the given equation by the pairs of equations as $x=3y-4,x=2y-5$. We see that these both represent a pair of straight lines. So the solution can be obtained from the y-coordinate of the point of intersection of these two lines, as shown below.