Question

What is the solution to the following system of linear equations x+y=5 x-y=1

Answer 1

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 :

$x+y=5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x-y=1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

We will be using the method of Elimination to solve the given system as follows :

Adding equations (i) and (ii), we get

$(x+y)+(x-y)=5+1\\\\\Rightarrow 2x=6\\\\\Rightarrow x=\dfrac{6}{2}\\\\\Rightarrow x=3.$

Substituting the value of x in equation (i), we get

$x+y=5\\\\\Rightarrow 3+y=5\\\\\Rightarrow y=5-3\\\\\Rightarrow y=2.$

Thus, the required solution of the given system is

x = 3  and  y = 2.

Answer 2

$\underline{+\left\{\begin{array}{ccc}x+y=5\\x-y=1\end{array}\right}\ \ \ |\text{add both sides of the equations}\\.\ \ \ \ \ \ \ 2x=6\ \ \ \ |:2\\.\ \ \ \ \ \ \ \ \ x=3\\\\\text{substitute the value of x to the first equation}\\\\3+y=5\ \ \ \ |-3\\y=2\\\\\text{Answer:}\ \ \ \boxed{x=3;\ y=2}\to(3;\ 2)$