Question

Solve for x and y:
3x + 4y = 55
5x + 2y = 45

• A. x = 10 , y = 5
• B. x = 1, y = 13
• C. x = 5 , y = 5
• D. x = 5, y = 10

Answer 1

The correct option is D x = 5, y = 10

Given the pair of equations:
3x + 4y = 55 --------- (i)
5x + 2y = 45 --------- (ii)

Multiply (ii) by 2:

10x + 4y = 90 -------- (iii)

Subtract (i) from (iii), we have:
10x - 3x = 90 - 55
$⟹$ 7x = 35
$⟹$ x = 5

Subtituing value of x in (i):
5(3) + 4y = 55
$⟹$ 4y = 55 - 15
$⟹$ 4y = 40
$⟹$ y = 10

Therefore,
x = 5 and y = 10