To solve the system of equations:

ax + by = a b÷2
3x + 5y = 4

We will use a method called substitution. Here's how we can solve it step by step:

Step 1: Solve the first equation for x in terms of y.
ax + by = a b÷2
ax = a b÷2 - by
x = (a b÷2 - by)/a

Step 2: Substitute the value of x from the first equation into the second equation.
3x + 5y = 4
3((a b÷2 - by)/a) + 5y = 4
(3a b÷2 - 3by)/a + 5y = 4

Step 3: Multiply through by 'a' to eliminate the fraction.
3a b÷2 - 3by + 5ay = 4a

Step 4: Simplify the equation.
(3a b - 6by + 10ay)/2a = 4a

Step 5: Multiply through by 2a to eliminate the denominator.
3a b - 6by + 10ay = 8a^2

Step 6: Rearrange the equation.
10ay - 6by = 8a^2 - 3a b

Step 7: Solve the equation for y.
y(10a - 6b) = 8a^2 - 3a b
y = (8a^2 - 3a b)/(10a - 6b)

Step 8: Substitute the value of y into the first equation to solve for x.
ax + by = a b÷2
ax + b((8a^2 - 3a b)/(10a - 6b)) = a b÷2
ax + (8a^2 b - 3a b^2)/(10a - 6b) = a b÷2

Step 9: Multiply through by (10a - 6b) to eliminate the denominator.
a(10a - 6b)x + (8a^2 b - 3a b^2) = a^2 b

Step 10: Simplify the equation.
10a^2 x - 6abx + 8a^2 b - 3a b^2 = a^2 b

Step 11: Rearrange the equation.
10a^2 x - 6abx = 3a b^2 - 8a^2 b

Step 12: Factor out x.
x(10a^2 - 6ab) = 3a b^2 - 8a^2 b
x = (3a b^2 - 8a^2 b)/(10a^2 - 6ab)

Step 13: Now we have the values of x and y in terms of a and b. Plug in the values of a and b to find the specific values of x and y.

Note: The solution to

X=1/2 and y=1/2