Answer
\[\left\{ \left( 4,1 \right) \right\}\]
Work Step by Step
To find the solution of provided system of equation by substitution method use the following steps:
Step1:
The second equation, \[x-4y=0\], solve it for the x in terms of y.
\[\begin{align}
& x-4y=0 \\
& x=4y
\end{align}\]
Step2:
Substitute the value of \[x=4y\] into the other equation\[2x+3y=11\]. The equation became in one variable y. Solve the equation for y.
\[\begin{align}
& 2x+3y=11 \\
& 2\left( 4y \right)+3y=11 \\
& 8y+3y=11 \\
& 11y=11
\end{align}\]
Simplify the above equation:
\[y=1\]
Step3:
Now, substitute the value of y obtained in step2, in \[x=4y\].
\[\begin{align}
& x=4y \\
& x=4\cdot 1 \\
& x=4 \\
\end{align}\]
Step4:
The value of x and y obtained in step2 and step3, is the solution of the provided system of equations.
Hence \[\left\{ \left( 4,1 \right) \right\}\]is the required solution.
Step5:
Now, to verify that the obtained solution is correct, substitute the values of x and y in both equations.
Put \[x=4\text{ and }y=1\]
\[\begin{align}
& 2x+3y=11 \\
& 2\cdot 4+3\cdot 1=11 \\
& 8+3=11 \\
& 11=11
\end{align}\]
\[\begin{align}
& x-4y=0 \\
& 4-4\cdot 1=0 \\
& 4-4=0 \\
& 0=0
\end{align}\]
Since, \[\left( 4,1 \right)\]satisfies both equations, the set \[\left( 4,1 \right)\]is the solution of the provided system of equations.
