Answer: The required solution is (x, y) = (4, 6).
Step-by-step explanation: We are given to solve the following system of equations :
[tex]x+3y=22~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2x-y=2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
From equation (ii), we have
[tex]2x-y=2\\\\\Rightarrow y=2x-2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Substituting the value of y from equation (iii) in equation (i), we get
[tex]x+3(2x-2)=22\\\\\Rightarrow x+6x-6=22\\\\\Rightarrow 7x=22+6\\\\\Rightarrow 7x=28\\\\\Rightarrow x=\dfrac{28}{7}\\\\\Rightarrow x=4.[/tex]
From equation (i), we get
[tex]4+3y=22\\\\\Rightarrow 3y=22-4\\\\\Rightarrow 3y=18\\\\\Rightarrowy=\dfrac{18}{3}\\\\\Rightarrow y=6.[/tex]
Thus, the required solution is (x, y) = (4, 6).
