Question

Solve the following simultaneous equation (show working).

[Q1) xy = 12]
[(x-1)(y+2)=15]


A. (x = 3, y = 4)

B. (x = 4, y = 3)

C. (x = 2, y = 6)

D. (x = 6, y = 2)

Answer 1

To solve the simultaneous equations, we can use the method of substitution. The solution to the simultaneous equations is x = 6 and y = 2.

Step-by-step explanation:

To solve the simultaneous equations, we can use the method of substitution. We can rearrange the first equation, xy = 12, to solve for x in terms of y, giving us x = 12/y. We can then substitute this value of x into the second equation to solve for y:

(12/y - 1)(y+2) = 15

Expanding and simplifying the equation gives us a quadratic equation:

12 - y + 12/y - 2 = 15

Combining like terms and rearranging, we have:

y^2 -3y - 2 = 0

Factoring the quadratic equation, we get:

(y - 2)(y - 1) = 0

Therefore, the possible values for y are 1 and 2. Substituting these values back into the first equation, we can solve for x:

For y = 1, x = 12/1 = 12

For y = 2, x = 12/2 = 6

So the solution to the simultaneous equations is x = 6 and y = 2.