solve for x and y: ax + by= a+b divided by 2 and 3x + 5y= 4

ax + by= a+b/2     ... (1)

3x + 5y= 4            ... (2)

Multiply (1) by 5,

5ax + 5by= 5(a+b)/2     ... (3)

Multiply (2) by b,

3bx + 5by= 4b              ... (4)

 

Subtracting (4) from (3), we get,

 

x(5a-3b) = 5a+5b-8b/2

x(5a-3b) = 5a+3b/2

x = 1/2

 

From (2):

5y = 4-3x = 4 - 3/2 = 5/2

y = 1/2