Question

hinking (10 Marks) 7. Solve the following system of equations algebraically (substitution or elimination). (6 marks) y = log ys(20x + 5) and y = 4 + log/s(2x - 1) 8. Every time a fluid is purified using a certain method of evaporation and condensation, 3.7% of it is lost. The fluid must be replaced before 40% has been lost, or the equipment it is being used in will be damaged. How many purifications can the fluid be put through before it must be replaced? (4 marks)

Answer 1

To solve the system of equations, use the elimination method and properties of logarithms. Begin by isolating 'y' in one of the equations, and then substitute it into the second equation. Simplify using logarithmic properties, and solve for 'y' by rewriting the equation in exponential form.

Step-by-step explanation:

To solve the system of equations using elimination, we'll start by isolating one variable in one of the equations. Let's isolate 'y' in the first equation, which gives us 'y = log ys(20x + 5)'. Next, we'll substitute this expression for 'y' in the second equation. We'll have 'log ys(20x + 5) = 4 + log/s(2x - 1)'. Now, we'll use properties of logarithms to rewrite the equation as 'log ys(20x + 5) - log/s(2x - 1) = 4'. By applying the logarithmic identity 'log a - log b = log(a/b)', we get 'log ys[(20x + 5)/(2x - 1)] = 4'. Since the base is not specified, we'll assume it's 10. Writing it in exponential form, we have '10^4 = ys[(20x + 5)/(2x - 1)]'. Solving for 'y', we divide both sides by 's' to get 'y = (10^4)/(ys[(20x + 5)/(2x - 1)])'. Both equations in the system are now solved for 'y'.

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