Solve the following pair of linear equations by the elimination method and the substiturio \( \frac{x}{2}+\frac{2 y}{3}=-1 \) and \( x-\frac{y}{3}=3 \)

9. An ice manufacturing machine requires 10 minutes to warm up before the production of ice begins. The weight, in tonnes, of ice produced varies directly as the number of hours of production. Given that 20 tonnes of ice are produced when the machine is run for half an hour, find the weight of ice manufactured when the machine is run for \( 1 \frac{3}{4} \) hours.

What is a rational exponent and how does it relate to radical expressions?

Solve the equation \( x: \log _{x+1}\left(x^{2}+x-6\right)^{2}=4 \) We have

Solve the equation: \( \sqrt{x + 4} = 6 \)

(i) \( \frac{x}{3}-\frac{4}{5}=\frac{(x-2)}{4} \)