[tex] \underline{+\left\{\begin{array}{ccc}x+y=5\\x-y=1\end{array}\right}\ \ \ |\text{add both sides of the equations}\\.\ \ \ \ \ \ \ 2x=6\ \ \ \ |:2\\.\ \ \ \ \ \ \ \ \ x=3\\\\\text{substitute the value of x to the first equation}\\\\3+y=5\ \ \ \ |-3\\y=2\\\\\text{Answer:}\ \ \ \boxed{x=3;\ y=2}\to(3;\ 2) [/tex]
Answer: The required solution of the given system is
x = 3 and y = 2.
Step-by-step explanation: We are given to find the solution to the following system of linear equations :
[tex]x+y=5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x-y=1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
We will be using the method of Elimination to solve the given system as follows :
Adding equations (i) and (ii), we get
[tex](x+y)+(x-y)=5+1\\\\\Rightarrow 2x=6\\\\\Rightarrow x=\dfrac{6}{2}\\\\\Rightarrow x=3.[/tex]
Substituting the value of x in equation (i), we get
[tex]x+y=5\\\\\Rightarrow 3+y=5\\\\\Rightarrow y=5-3\\\\\Rightarrow y=2.[/tex]
Thus, the required solution of the given system is
x = 3 and y = 2.
