Answer :
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
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
Answer:
x = 1/2 and y =1/2
Step-by-step explanation:
⇒ ax + by = a + b/2 ----- ( 1 )
⇒3x + 5y = 4 ----- ( 2 )
Multiplying equation ( 1 ) by 5, we get
⇒5ax + 5by = 5(a + b)/2 ------ ( 3 )
Multiplying equation ( 2 ) by b, we get
⇒3bx + 5by = 4b ----- ( 4 )
Subtracting equation ( 4 ) from ( 3 ), we get
⇒(5a − 3b)x = 5a + 5b − 8b/2
⇒(5a − 3b)x = (5a − 3b)/2
⇒x = (5a − 3b)/2 × 1/(5a − 3b)
∴x = 1/2
Substituting value of x in equation ( 2 ) we get,
⇒3 × 1/2 + 5y = 4
⇒3/2 + 5y = 4
⇒5y = 4 − 3/2
⇒5y = 5/2
∴y = 1/2
∴ Values of (x, y) are (1/2 ,1/2)