Answer
\[\left\{ \left( 5,1 \right) \right\}\]
Work Step by Step
To find the solution of provided system of equation by substitution method use the following steps:
Step1:
The second equation, \[y=2x-9\], is solved for the y in terms of x.
Step2:
Substitute the value of \[y=2x-9\] into the other equation\[x+3y=8\]. The equation became in one variable x. Solve the equation for x.
\[\begin{align}
& x+3y=8 \\
& x+3\left( 2x-9 \right)=8 \\
& x+6x-27=8 \\
& 7x=27+8
\end{align}\]
Simplify the above equation:
\[\begin{align}
& 7x=27+8 \\
& 7x=35 \\
& x=5
\end{align}\]
Step3:
Now, substitute the value of x obtained in step2, \[y=2x-9\]:
\[\begin{align}
& y=2x-9 \\
& y=2\cdot 5-9 \\
& y=10-9 \\
& y=1
\end{align}\]
Step4:
The value of x and y obtained in step2 and step3, is the solution of the provided system of equations.
Hence \[\left\{ \left( 5,1 \right) \right\}\]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 \[x=5\text{ and }y=1\]
\[\begin{align}
& x+3y=8 \\
& 5+3\cdot 1=8 \\
& 5+3=8 \\
& 8=8
\end{align}\]
\[\begin{align}
& y=2x-9 \\
& 1=2\cdot 5-9 \\
& 1=10-9 \\
& 1=1
\end{align}\]
Since, \[\left( 5,1 \right)\]satisfies both equations, the set \[\left\{ \left( 5,1 \right) \right\}\]is the solution of the provided system of equations.
