Final answer:
To solve the system of equations 5xy = 24 and xy = 4, we can use the substitution method. The solution to the system of equations is x = 4.8 and y = 5/6.
Step-by-step explanation:
To solve the system of equations 5xy = 24 and xy = 4, we can use the substitution method.
Step 1: Solve one of the equations for one variable in terms of the other. From the second equation, we can solve for x in terms of y as x = 4/y.
Step 2: Substitute the expression for x in terms of y from step 1 into the other equation. We substitute 4/y for x in the first equation, giving us (5(4/y))y = 24.
Step 3: Simplify and solve for y. Multiplying 5(4/y)y gives us 20 = 24y. Dividing both sides by 24, we find that y = 20/24 = 5/6.
Step 4: Substitute the value of y into one of the original equations to solve for x. Substituting y = 5/6 into xy = 4 gives us (x)(5/6) = 4. Solving for x, we find x = 24/5 = 4.8.
Therefore, the solution to the system of equations is x = 4.8 and y = 5/6.