Check which of the following are the solutions of the equation 5x – 4y = 20.
(i) $(4,0)$
(ii) $(0,5)$
(iii) $\left(-2, \frac{5}{2}\right)$
(iv) $(0,-5)$
(v) $\left(2, \frac{-5}{2}\right)$
The equation given is 5x – 4y = 20.
(i) (4, 0)
Putting the value in the given equation we have
LHS : $5(4)-4(0)=20$
RHS : 20
LHS = RHS
Thus, (4, 0) is a solution of the given equation.
(ii) (0, 5)
Putting the value in the given equation we have
LHS : $5(0)-4(5)=0-20=-20$
RHS : 20
$\mathrm{LHS} \neq \mathrm{RHS}$
Thus, (0, 5) is not a solution of the given equation.
(iii) $\left(-2, \frac{5}{2}\right)$
Putting the value in the given equation we have
LHS : $5(-2)-4\left(\frac{5}{2}\right)=-10-10=-20$
RHS : 20
LHS $\neq$ RHS
Thus, $\left(-2, \frac{5}{2}\right)$ is not a solution of the given equation.
(iv) (0, –5)
Putting the value in the given equation we have
LHS : $5(0)-4(-5)=0+20=20$
RHS : 20
LHS = RHS
Thus, (0, –5) is a solution of the given equation.
(v) $\left(2, \frac{-5}{2}\right)$
Putting the value in the given equation we have
LHS : $5(2)-4\left(\frac{-5}{2}\right)=10+10=20$
RHS : 20
$\mathrm{LHS}=\mathrm{RHS}$
Thus, $\left(2, \frac{-5}{2}\right)$ is a solution of the given equation.