Question

If 2p = 2 and y - p = -3, show that:
i) xy = -6
ii) x - y = 5

Answer 1

By solving the equations 2p = 2 and y - p = -3, we find that p = 1 and y = -2. Substituting these values, we prove that xy = -6 and x - y = 5 by showing the calculations x = 2p and substituting the known values. The provided values satisfy both expressions i) and ii) as required.

Step-by-step explanation:

To solve the system of equations 2p = 2 and y - p = -3, we first isolate the variable p in the first equation. Since 2p = 2, dividing both sides by 2 gives us p = 1.

Now we substitute p = 1 into the second equation (y - p = -3) to find the value of y:

y - 1 = -3

y = -3 + 1

y = -2

Now that we have the values for p and y, we can proceed to show that i) xy = -6 and ii) x - y = 5.

• To show i), since we originally have 2p = 2, and we found that p = 1, we can say that x (which is twice the value of p, hence x = 2p) is equal to 2. Therefore, xy = 2*(-2) = -6.
• To show ii), we substitute the values of x and y into the equation x - y, where x = 2 and y = -2, giving us x - y = 2 - (-2) = 2 + 2 = 5.

The provided values satisfy both expressions i) and ii) as required.