Check whether x = 2 and y = 3 the solution of the pair of linear equations: `x-3y = 2, 6y - 2x = 5`

Answer

To check whether \( x = 2 \) and \( y = 3 \) is a solution of the pair of linear equations:

1. **First Equation: \( x - 3y = 2 \)**

Substitute \( x = 2 \) and \( y = 3 \) into the equation:
\[ 2 - 3(3) = 2 \]
Calculate the left-hand side:
\[ 2 - 9 = -7 \]
Now, compare with the right-hand side:
\[ -7 \neq 2 \]
Therefore, \( x = 2 \) and \( y = 3 \) is **not a solution** for the first equation.

2. **Second Equation: \( 6y - 2x = 5 \)**

Substitute \( x = 2 \) and \( y = 3 \) into the equation:
\[ 6(3) - 2(2) = 5 \]
Calculate the left-hand side:
\[ 18 - 4 = 14 \]
Now, compare with the right-hand side:
\[ 14 \neq 5 \]
Therefore, \( x = 2 \) and \( y = 3 \) is **not a solution** for the second equation.

In conclusion, \( x = 2 \) and \( y = 3 \) is **not a solution** for the pair of linear equations.