Question

How do you solve the simultaneous equations $ 2x - 3y = 11 $ and $ 5x + 2y = 18 $ ?

Answer 1

Hint: In order to solve this question ,use elimination method to eliminate x by multiplying whole first equation with 5 and the second equation with 2 and subtract both equations to eliminate x and solve for y , after getting value of y we substitute in any one of the equations to get value of x.

Complete step-by-step answer:
Given a couple of simultaneous linear equation
 $ 2x - 3y = 11 $ -(1)
 $ 5x + 2y = 18 $ -(2)
Multiplying equation (1) with the coefficient of x in the equation (2) and Multiplying equation (2) with the coefficient of x in equation (1).
 $
  5 \times (2x - 3y) = 5 \times (11) \\
   \Rightarrow 10x - 15y = 55\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - (3) \;
  $
 $
  2 \times (5x + 2y) = 2 \times (18) \\
   \Rightarrow 10x + 4y = 36\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - (4) \;
  $
Now subtraction equation (4) from equation (3)
 $
  10x - 10x - 15y - 4y = 55 - 36 \\
   - 19y = 19 \\
  y = \dfrac{{ - 19}}{{19}} \\
  y = - 1 \;
  $
Hence value of y is equal to -1
Now putting this value of y in either equation (1) or (2) to find out the value of x
We are putting into equation (1).So,
 $
  2x - 3( - 1) = 11 \\
  2x + 3 = 11 \\
  2x = 11 - 3 \\
  2x = 8 \\
  x = \dfrac{8}{2} \\
  x = 4 \;
  $
Therefore ,solution to the simultaneous linear equation is $ x = 4 $ and $ y = - 1 $
So, the correct answer is “ $ x = 4 $ and $ y = - 1 $ ”.

Note: 1. The Elimination Method: Elimination is one the simple method by which one can solve a couple of simultaneous linear equations. Using this method either add or subtract the equations to obtain an equation which is having only one variable.
When the sign of the coefficient of the variable you wish to eliminate are reversed, we try to add the equations and when the sign of the coefficients are the same we subtract each other to eliminate the desired variable .