The given system of equations has only one solution
Solution:
Given system of equations are:
2y = x - 9 ------- eqn 1
5x - 4y = 18 ------- eqn 2
Let us first solve the system of equations
From eqn 1,
x = 2y + 9 ----- eqn 3
Substitute eqn 3 in eqn 2
5(2y + 9) - 4y = 18
10y + 45 - 4y = 18
6y = 18 - 45
6y = -27
[tex]y = \frac{-27}{6}\\\\y = \frac{-9}{2}[/tex]
Substitute the value of "y" in eqn 3
[tex]x = 2( \frac{-9}{2}) + 9\\\\x = -9 + 9\\\\x = 0[/tex]
Thus [tex](x, y) = (0, \frac{-9}{2})[/tex]
Thus the given system of equations has only one solution
