can anybody help me solve this simultaneous equation question....plz?

Question

5x + 3y = 5
2/x - 3/y = 2

Answer 1

Use the first equation to get x = f(y)
5x+3y = 5
5x = 5 - 3y
x = 1 -3y/5

Replace x by 1-3y/5 in second equation
2/(1-3y/5) - 3/y = 2
(2y - 3(1-3y/5))/(y(1-3y/5) = 2
2y - 3 +9y/5 = 2y(1-3y/5)
19y/5 - 3 = 2y - (6/5)y^2
(6/5)y^2 + 19y/5 - 2y - 3 = 0
(6/5)y^2 + (9/5)y - 3 = 0

Solve for y

y1 = 1 or y2= 0.4
then compute x = 1 -3y/5
x1 = -2.5 or x2 = 2.5

Solutions are {x1,y1} and {x2,y2}

Answer 2

Okay, this is ugly without mathtype, but I'll try.
This is by substitution
Step 1. Solve one of the equations for one of the variables.
I chose to solve the top equation for x, but it doesn't matter which equation or variableyou choose. Some are just uglier than others...
5x + 3y = 5
Subtract 3y from each side
5x = 5 - 3y
Divide by 5 on each side
x = (5-3y)/5

Step 2. Substitute the value from Step 1 for the variable in the other equation.

2/ ((5-3y)/5) - 3/y = 2
Simplify the first term by multiplying by (5/(5-3y))/(5/(5-3y))
10 / (5-3y) - 3/y = 2
find equivalent fractions with a common denominator for the two fractional quantities on the left
10y/(y(5-3y) - (3(5-3y))/(y(5-3y)) = 2
Multiply by the denominator on both sides
10y - 3(5-3y) = 2(5-3y)
Expand with distribution
10y+ -15 + 9y = 10 + -6y
Collect like terms
19y + -15 = 10 + -6y
Add 6y to each side
25y + 15 = 10
Add -15 to both sides
25y = -5
Divide by 25
y = -1/5

Step 3. Substitute value found in Step 2 into one of the equations and solve for x.
I chose the top equation, but again, either one will do.

5x + 3 (-1/5) = 5
Simplify
5x + -(3/5) = 5
Add 3/5 to each side (I made it an improper fraction at the same time)
5x = (28/5)
Divide by 5
x = 28/25

There you go...x = 28/25, y = -1/5...
The answer is (28/25, -1/5)

Answer 3

2/x - 3/y = 2
2y - 3x = 2xy

5x + 3y = 5
5x = 5 - 3y
x = 1 - 3/5y

2y - 3(1 - 3/5y) = 2(1 - 3/5y)y
2y - 3 + 9/5y = 2y - 6/5y²
10y - 15 + 9y = 10y - 6y²
19y - 15 = 10y - 6y²
6y² + 9y - 15 = 0
2y² + 3y - 5 = 0
(2y + 5)(y - 1) = 0

2y = -5
y = -5/2

or

y = 1

5x + 3y = 5
5x + 3(-5/2) = 5
5x - 15/2 = 5
x - 3/2 = 1
x = 5/2

5x + 3y = 5
5x + 3(1) = 5
5x + 3 = 5
5x = 2
x = 2/5

Solutions:

x = 2/5, y = 1
x = 5/2, y = -5/2