Question

Solve the following pair of equations by the elimination method.
 \[
  x + y = 14 \\
  x - y = 4 \\
 \]

Answer 1

Hint: In this question from two equations we can see the coefficient of the variable are equal but their sign is different so we will add both equation to eliminate variable y and then we can find the variable x after which substituting the variable x in the original equation we can find the variable y.

Complete step-by-step answer:
Given the equations
 \[
\Rightarrow x + y = 14 - - (i) \\
\Rightarrow x - y = 4 - - (ii) \;
 \]
From the above equations we can see the coefficient of variable y is equal but are different in sign, so by elimination rule we will add both the equations
Adding equation (i) and (ii)
 \[
   \underline
\Rightarrow + x + y = 14 \\
\Rightarrow + x - y = 4 \\
   \\
   + 2x = 18 \;
 \]
Hence the value of the variable x will be
 \[
\Rightarrow x = \dfrac{{18}}{2} \\
   = 9 \;
 \]
Now we will substitute the value of variable x in the equation (i) to find the value of the variable y, we can write
 \[
\Rightarrow x + y = 14 \\
\Rightarrow \left( 9 \right) + y = 14 \\
\Rightarrow y = 14 - 9 \\
\Rightarrow y = 5 \;
 \]
Hence the value of the variable \[y = 5\] .
So, the correct answer is “x=9, y=5”.

Note: Elimination methods are generally used to find the values of the variable of linear equations, this method is done by either adding or subtracting the linear equations to get an equation in one variable. Students must note the elimination method is generally used to remove one of the variables so to get a simplified equation and then to find the values of these variables one by one.