Question

Solve the following simultaneous equation.
5x + 2y = –3; x + 5y = 4

Answer 1

5x + 2y = –3                      .....(I)
x + 5y = 4                                .....(II)   
Multiply (II) with 5 we get
5x + 25y = 20                          .....(III)
Subtracting (III) from (I) we get
\[5x - 5x + 2y - 25y = - 3 - 20\]
\[ \Rightarrow - 23y = - 23\]
\[ \Rightarrow y = \frac{- 23}{- 23} = 1\]
Putting the value of y = 1 in (II) we get
\[x + 5\left( 1 \right) = 4\]
\[ \Rightarrow x + 5 = 4\]
\[ \Rightarrow x = 4 - 5 = - 1\]
Thus, (x, y) = (−1, 1)