Question

What is the solution of the equations $x - y = 0.9$ and $11{\left( {x + y} \right)^{ - 1}} = 2?$
A. $x = 3.2,y = 2.3$
B. $x = 1,y = - 0.1$
C. $x = 2,y = 1.1$
D. $x = 1.2,y = 0.3$

Answer 1

Hint: The questions listed above are expressed as a nonlinear equation. It has two variables simplified to get the answer to the given query. Assuming the value from one of the variables. we understand that a straight line is the geometric or representation of linear equations in two variables.

Formula Used:
Linear equations in one variable,
$ax + b = 0$
where $a$ and $b$ are two integers, and $x$ is a variable
Linear equation in two variables,
$ax + by = r$
$a,b,r$ are real numbers,
If $a$ and \[b\] are not both equal to $0$
$x$ and $y$ are the two variables.

Complete step-by-step answer:
Given by,
$
  x - y = 0.9 \\
  11{\left( {x + y} \right)^{ - 1}} = 2 \\
 $
The two variables of linear equations,
$x - y = 0.9$……………$(1)$
$11{(x + y)^{ - 1}} = 2$
To simplify the above equation,
$\dfrac{{11}}{{x + y}} = 2$
Rearrange the above equation,
We get,
$2x + 2y = 11$……………$(2)$
Multiply $(1)$ by $2$
Here,
$2x - 2y = 1.8$
Added the above two equations,
We get,
$4x = 12.8$
Simplifying the equation,
Find the $x$ value,
$\Rightarrow$ \[x = 3.2\]
Substitute a given $x$ value in equation $(1)$
$x - y = 0.9$
Then,
$\Rightarrow$ \[y = 0.9 - 3.2\]
Subtracts the above equation,
$\Rightarrow$ $y = 2.3$
Hence, the option A is the correct answer $x = 3.2,y = 2.3$.

Note: A linear equation with two variables is an equation with two distinct alternatives. If the two linear equations have the same slope value, then there are no solutions to the equations. Since the lines are parallel and don't overlap with each other. It is possible to define the solution and then try to find the other solution. There are infinitely many solutions in two variables, for a single linear equation.