Question

How do you find the solution of the system of equations $3x+4y=10$ and $x-y=1$?

Answer 1

Solve the equations $\mathbf{3}\mathit{x}\mathbf{+}\mathbf{4}\mathit{y}\mathbf{=}\mathbf{10}$ and $\mathit{x}\mathbf{-}\mathit{y}\mathbf{=}\mathbf{1}$.

Consider the equation :- $x-y=1$

Rewrite this equation as following :

$\begin{array}{rcl}x-y& =& 1\\ & \Rightarrow & x=y+1\end{array}$

Put this value in the other equation gives :

$\begin{array}{rcl}3(y+1)+4y& =& 10\\ & \Rightarrow & 3y+3+4y=10\\ & \Rightarrow & 7y=10-3\\ & \Rightarrow & 7y=7\\ & \Rightarrow & y=\frac{7}{7}\\ & \Rightarrow & y=1\end{array}$

Then put this value of $y$ in $x=y+1$:

$\begin{array}{rcl}x& =& 1+1\\ & \Rightarrow & x=2\end{array}$

Therefore, the required solution of the given system of equations is $\mathit{x}\mathbf{=}\mathbf{2}\mathbf{,}\mathit{y}\mathbf{=}\mathbf{1}$.