Answer
\[\left\{ \left( 2,4 \right) \right\}\]
Work Step by Step
To find the solution of provided system of equation by substitution method use the following Step s:
Step 1:
The second equation, \[y=2x\], is solved for the y in terms of x.
Step 2:
Substitute the value of \[y=2x\] into the other equation\[x+y=6\]. The equation became in one variable x. Solve the equation for x.
\[\begin{align}
& x+y=6 \\
& x+2x=6 \\
& 3x=6 \\
& x=2
\end{align}\]
Step 3:
Now, substitute the value of x obtained in step 2 in \[y=2x\].
\[\begin{align}
& y=2x \\
& y=2\cdot 2 \\
& y=4
\end{align}\]
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 \[\left\{ \left( 2,4 \right) \right\}\]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 \[x=2\text{ and }y=4\]
\[\begin{align}
& x+y=6 \\
& 2+4=6 \\
& 6=6
\end{align}\]
\[\begin{align}
& y=2x \\
& 4=2\cdot 2 \\
& 4=4
\end{align}\]
Since, \[\left( 2,4 \right)\]satisfies both equations, the set \[\left\{ \left( 2,4 \right) \right\}\]is the solution of the provided system of equations.
