Question

Solve the following simultaneous equations. 2/x 2/3y=1/6 ; 3/x 2/y=0

a. x=1,y=1
b. x=2,y=2
c. x=3,y=3
d. x=4,y=4

Answer 1

To solve the simultaneous equations, we can use a method called elimination. After simplifying and rearranging, we find that x = 1 and y = 1.

Step-by-step explanation:

To solve the simultaneous equations 2/x + 2/3y = 1/6 and 3/x + 2/y = 0, we can use a method called elimination. Here are the steps:

1. Multiply the first equation by 6 to get rid of the denominators: 12/x + 4/3y = 1
2. Multiply the second equation by 3 to get rid of the denominators: 9/x + 6/y = 0
3. Now, subtract the second equation from the first equation to eliminate the x variable: (12/x - 9/x) + (4/3y - 6/y) = 1 - 0
4. Simplify the equation: 3/x - 2/y = 1
5. Now, we have a new equation with only one variable. Multiply both sides by xy to eliminate the denominators: 3y - 2x = xy
6. Rearrange the equation to isolate y: 3y - xy = 2x
7. Factor out y on the left side: y(3 - x) = 2x
8. Divide both sides by (3 - x) to solve for y: y = 2x / (3 - x)

Therefore, we have solved the equations and found that x = 1 and y = 2 / (3 - 1) = 1.