Question

Solve the equation:
$x + y = 14$ and $x - y = 4$
A.$x = 9,\,y = 5$
B.$x = 9,\,y = 11$
C.$x = 9,\,y = 4$
D.$x = 9,\,y = 6$

Answer 1

Hint: The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it

Complete step-by-step answer:
Given equations are $x + y = 14$ and $x - y = 4$.
Now, to solve the equation we need to add both the equations.
So,
$
\Rightarrow x + y = 14 \\
\Rightarrow x - y = 4 \\
   \\
\Rightarrow 2x = 18 \\
\Rightarrow x = \dfrac{{18}}{2} \\
\Rightarrow x = 9 \;
 $
Now, as x value is equal to 9, so now to find the value of y, we need to use the value of x, so substitute 9 for x, in any of the given two equations.
So, $x + y = 14$.
$
\Rightarrow 9 + y = 14 \\
\Rightarrow y = 14 - 9 \\
\Rightarrow y = 5 \;
 $
So, the value of y will be 5 and the value of x is 9.
Therefore, on solving the equations $x + y = 14$ and $x - y = 4$, we get the value of y will be 5 and the value of x is 9.
So, the correct answer is “x=9,y=5”.

Note: This question can be solved in another way.
As, the given equation is $x + y = 14$ and $x - y = 4$.
Now, write the first equation in for y in the terms of x.
So, $x + y = 14$ can be written as $y = 14 - x$.
Now, use the above value of y in the second given equation.
$
  x - y = 4 \\
  x - \left( {14 - x} \right) = 4 \\
  x - 14 + x = 4 \\
  2x - 14 = 4 \\
  2x = 4 + 14 \\
  2x = 18 \\
  x = \dfrac{{18}}{2} \\
  x = 9 \;
 $
Now, use this value in any given equation, So, $x + y = 14$, now substitute the value of x as 9 in the equation $x + y = 14$.
$
  x + y = 14 \\
  9 + y = 14 \\
  y = 5 \;
 $
Therefore, on solving the equations $x + y = 14$ and $x - y = 4$, we get the value of y will be 5 and the value of x is 9.