Question

Solve the following sets of simultaneous equations.
$
  3x - 5y = 16 \\
  x - 3y = 8 \\
 $

Answer 1

Hint: Here, we will first convert coefficients of one variable common for both the given equations. Then will use the elimination method to find the values for the unknown terms’ “x” and “y”.

Complete step by step solution:
Given Expression:
$3x - 5y = 16$ …… (A)
$x - 3y = 8$ …… (B)
Multiply the equation (B) with the number
$3x - 9y = 24$ ….. (C)
Subtract equation (C ) from the equation (A)
$(3x - 5y) - (3x - 9y) = 16 - 24$
Open the brackets, remember when there is a negative sign outside the bracket then the sign of the terms inside the bracket’s changes. Positive terms become negative and vice-versa.
$3x - 5y - 3x + 9y = 16 - 24$
Like terms with the same value and opposite sign cancel each other.
$ - 5y + 9y = 16 - 24$
Find the difference in the above equation, when you subtract, give a sign of the bigger number.
$4y = - 8$
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
$y = - \dfrac{8}{4}$
Common multiple from the numerator and the denominator cancels each other.
$y = ( - 2)$ ….. (D)
Place the above value in the equation (B)
$x - 3y = 8$
$x - 3( - 2) = 8$
Product of two negative terms gives the positive term.
$
  x + 6 = 8 \\
  x = 8 - 6 \\
  x = 2 \\
 $
Hence, the required solution is $(x,y) = (2, - 2)$.

Note:
Be careful about the sign convention, when you add and subtract between two same and different signs. When you add two positive terms the resultant value is in positive and when you add two negative terms then the resultant value is in negative. When you add two terms with two different signs then the sign will be of the bigger number to the resultant value.