Question

We are given $x + y = 10$ and $x - y = 2$ , find $x$ .

Answer 1

Hint: There are two linear equations and two unknowns. It is easy to calculate the value of unknowns. Solving these will be easy as it has one as its coefficient.
To find x we need to do the elimination method.
Elimination method:
We will add or subtract both equations to eliminate one variable and get the value of one variable.

Complete step by step answer:
Given,
There are two linear equations, i.e,
$x + y = 10$
$x - y = 2$
We can eliminate y, to find the value of x.
Let the $x + y = 10$ be the equation $1$ and
$x - y = 2$ be equation $2$
By adding this equation, $y$ gets eliminated, it will be easy to find the value of x,
The equation $1$ and the equation $2$ gets added, we will get the value of x.
$1 + 2 \Rightarrow x + y + x - y = 10 + 2$
The y terms get canceled as it has the same coefficient and opposite sign of the equation,
$2x = 10 + 2$
Add the values on the right side of the equation,
$2x = 12$
$x = \dfrac{{12}}{2}$
Divide the numerator and denominator of the equation,
$x = 6$
The value of x is $6$ .

Note:
 We can find the value of x by substitution method as well. We will substitute value of y from one equation to another such as-
From eq.2 -
y =x -2
Then substitute y in eq.1,
$
  x + x - 2 = 10 \\
  2x = 12 \\
  x = 6 \\
 $
The value of x is $6$ .