Question

Solve the following simultaneous equation.

x + 7y = 10; 3x – 2y = 7

Answer 1

x + 7y = 10                               ...(I)
3x – 2y = 7                               ...(II)  

Multiply equation (I) by 3,
3x + 21y = 30                          ...(III)

Subtracting (II) from (III), we get,
\[\begin{array}{l}  
\phantom{\texttt{0}}\texttt{ 3x + 21y = 30}\\ \phantom{\texttt{}}\texttt{– 3x – 2y  = 7}\\ \hline\phantom{\texttt{}}\texttt{ (-)  (+)  (-)}\\ \hline \end{array}\]

∴ 23y  = 23

∴ y = `23/23` 

∴ y = 1

Putting the value of y = 1 in (II), we get,
3x – 2y = 7
∴ 3x – 2(1) = 7
∴ 3x – 2 = 7
∴ 3x = 7 + 2
∴ 3x = 9
∴ x = `9/3`
∴ x = 3
Thus, (x, y) = (3, 1).