Question

Solve for x and y
$ax \: + \: by \: = \: (a \: + \: b) \div 2$
$3x \: + \: 5y \: = \: 5$

Answer 1

Answer:

*If 5a-3b=0 ---> 3x+5y=4 -->  

S={ (x, (4-3x)/5) ,, xis in R}  

*Else 5a-3b≠0  

ax+by=s --> 5ax+5by=5s  

3x+5y=4 --> 3bx+5by=4b --> (5a-3b)x=(5s-4b) -->  

(5a-3b)x=(5a-3b)/2 --> x=1/2  

y= (4-3/2)/5 =1/2 --> S=(1/2, 1/2)

Answer 2

check the attachment