Question

How do you solve the system of linear equations $5x-4y=9$ and $x-2y=-3$?

Answer 1

Hint: Simplify the first equation and try to find the value of ‘x’ in terms of ‘y’. Then put the value of ‘x’ obtained earlier to get the value of ‘y’. After getting the value of ‘y’ put that value in any of the equations to get the value of ‘x’.

Complete step by step solution:
Solving the system of linear equations: First we have to take any one of the two equations. Then we have to find the value of ‘x’ in terms of ‘y’. Putting that value of ‘x’ in the second equation we can get the value of ‘y’. Again putting that value of ‘y’ in any of the equations we can get the value of ‘x’.
Considering the first equation
$5x-4y=9$
From here ‘x’ can be obtained in terms of ‘y’ as
$\begin{align}
  & 5x=9+4y \\
 & \Rightarrow x=\dfrac{9+4y}{5} \\
\end{align}$
Now considering the second equation $x-2y=-3$
It can be written as
$\Rightarrow 2y=x+3$
Putting the value of ‘x’ we got earlier in the above equation, we get
$\begin{align}
  & \Rightarrow 2y=\dfrac{9+4y}{5}+3 \\
 & \Rightarrow 2y=\dfrac{9+4y+15}{5} \\
 & \Rightarrow 2y\times 5=24+4y \\
 & \Rightarrow 10y-4y=24 \\
 & \Rightarrow 6y=24 \\
 & \Rightarrow y=\dfrac{24}{6} \\
 & \Rightarrow y=4 \\
\end{align}$
Putting the value of ‘y’ in the second equation, we get
$\begin{align}
  & x-2y=-3 \\
 & \Rightarrow x-2\times 4=-3 \\
 & \Rightarrow x-8=-3 \\
 & \Rightarrow x=-3+8 \\
 & \Rightarrow x=5 \\
\end{align}$

Hence the solution of the system of linear equations $5x-4y=9$ and $x-2y=-3$ is $\left( x,y \right)=\left( 5,4 \right)$.

Note: We can also solve the linear equations by the coefficient of one of the variables equal. We just have to multiply suitable constants with both the equations to make the coefficient of one variable equal. Then we have to add or subtract the equation accordingly. From there we can get the value of one variable and putting that value in one of the given equations we can obtain the value of another.