Question

if 13x+19y=90 and 19x+13y=70 then x+y= _____​

Answer 1

Answer:

$19 \times (13x + 19y) = 19 \times 90$

$13 \times (19x + 13y) = 13 \times 70$

substracting 1st & 2nd, we get

$y( {19}^{2} - {13}^{2} ) = 1710 - 910 = 800$

$y = \frac{800}{32 \times 6} = \frac{25}{6}$

now putting y in 1st eq,

$13x + 19 \times \frac{25}{6} = 90$

$13x = 90 - \frac{475}{6} = \frac{65}{6}$

$x= \frac{65}{6 \times 13} = \frac{65}{78}$

so

$x + y = \frac{65}{78} + \frac{25}{6} = \frac{65 + 325}{78} = \frac{390}{78}$