Question

Solve the following simultaneous equations.
$
  5x - 3y = 8 \\
  3x + y = 2 \\
 $

Answer 1

Hint: Here, we are given two simultaneous equations and to get the values of the unknown terms “x” and “y” first convert the coefficient of any one variable common in both the equations and use the elimination method to get the required values.

Complete step-by-step solution:
Given expressions:
$\Rightarrow 5x - 3y = 8$ …. (A)
$\Rightarrow 3x + y = 2$ …. (B)
Now, multiply the equation (B) with the number
$\Rightarrow 9x + 3y = 6$ …. (C )
Now, Add equations (A) and (C)
$\Rightarrow 5x - 3y + 9x + 3y = 8 + 6$
Like terms with the same value and the opposite sign cancels each other.
$\Rightarrow 5x + 9x = 8 + 6$
Simplify the above equation finding the sum of the terms on both the sides of the equation –
$\Rightarrow 14x = 14$
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
$\Rightarrow x = \dfrac{{14}}{{14}}$
Common term from the numerator and the denominator cancels each other.
$ \Rightarrow x = 1$ …. (D)
Place the above value in the equation (B)
$\Rightarrow 3(1) + y = 2$
Make the required term the subject, when you move any term from one side to the another then the sign of the terms also changes. The positive term becomes negative and vice-versa.
$
   \Rightarrow y = 2 - 3 \\
   \Rightarrow y = - 1 \\
 $

Hence, the required solution is $(x,y) = (1, - 1)$



Note: Always be careful about the sign convention while simplifying the given two equations. To use the elimination method the coefficient of one of the variables should be the same, it may be with the same or the opposite signs. With respect to the signs to eliminate we have to use addition or subtraction to get one like term to remove.