Question

How do you solve the system of linear equations $5x-4y=7$ and $2y+6x=22$?

Answer 1

Hint: Try to find the value of ‘x’ in terms of ‘y’ from the first equation. Put the value of ‘x’ in the second equation 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
$5x-4y=7$
From here ‘x’ can be obtained in terms of ‘y’ as
$\begin{align}
  & 5x=7+4y \\
 & \Rightarrow x=\dfrac{7+4y}{5} \\
\end{align}$
Now considering the second equation $2y+6x=22$
It can be written as
$\Rightarrow 2y=22-6x$
Putting the value of ‘x’ we got earlier in the above equation, we get
$\begin{align}
  & \Rightarrow 2y=22-6\times \dfrac{7+4y}{5} \\
 & \Rightarrow 2y=\dfrac{110-6\left( 7+4y \right)}{5} \\
 & \Rightarrow 2y\times 5=110-42-24y \\
 & \Rightarrow 10y+24y=68 \\
 & \Rightarrow 34y=68 \\
 & \Rightarrow y=\dfrac{68}{34} \\
 & \Rightarrow y=2 \\
\end{align}$
Putting the value of ‘y’ in the second equation, we get
$\begin{align}
  & 2y+6x=22 \\
 & \Rightarrow 2\times 2+6x=22 \\
 & \Rightarrow 4+6x=22 \\
 & \Rightarrow 6x=22-4 \\
 & \Rightarrow x=\dfrac{18}{6} \\
 & \Rightarrow x=3 \\
\end{align}$

Hence the solution of the system of linear equations $5x-4y=7$ and $2y+6x=22$ is $\left( x,y \right)=\left( 3,2 \right)$.

Note: Another method of solving linear equations is by making the coefficient of one of the variables equal, by multiplying required constants with both the equations. Subtracting them one value can be obtained and putting that value in any equation other value can also be obtained.