Answer
\[\left\{ \left( 1,3 \right) \right\}\]
Work Step by Step
To find the solution of provided system of equation by substitution method use the following steps.
Step 1:
The second equation, \[y=3x\], is solved for the y in terms of x.
Step 2:
Substitute the value of \[y=3x\] into the other equation\[x+y=4\]. The equation became in one variable x. Solve the equation for x.
\[\begin{align}
& x+y=4 \\
& x+3x=4 \\
& 4x=4 \\
& x=1
\end{align}\]
Step 3:
Now, substitute the value of xobtained in step 2, \[y=3x\].
\[\begin{align}
& y=3x \\
& y=3\cdot 1 \\
& y=3
\end{align}\]
Step 4:
The value of x and y obtained in step 2 and step 3, is the solution of the provided system of equations.
Hence \[\left\{ \left( 1,3 \right) \right\}\]is the required solution.
Step 5:
Now, to verify that the obtained solution is correct, substitute the values of x and y in both equations.
Put \[x=1\text{ and }y=3\]
\[\begin{align}
& x+y=4 \\
& 1+3=4 \\
& 4=4
\end{align}\]
\[\begin{align}
& y=3x \\
& 3=3\cdot 1 \\
& 3=3
\end{align}\]
Since, \[\left( 1,3 \right)\]satisfies both equations, the set \[\left\{ \left( 1,3 \right) \right\}\]is the solution of the provided system of equations.
