Question

Solve for x and y , 86x+63y=241,63x+86y=215

Answer 1

Given Equation is :

= > 86x + 63y = 241    ------ (1)

= > 63x + 86y = 215    ------ (2)

Now,

On multiplying (1) * 63, we get

= > 5418x + 3969y = 15183    ------ (3)

On multiplying (2) * 86, we get

= > 5418x + 7396y = 18490    ------ (4)

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On solving (3) & (4), we get

= > 5418x + 3969y = 15183    

= > 5418x + 7396y = 18490

    ---------------------------------

                      3427y = 3307

                               y = 3307/3427.

Substitute y in (3), we get

= > 5418x + 3969y = 15183

= > 5418x + 3969(3307/3427) = 15183

= > 5418x = (38906658/3427)

= > x = 7181/3427.

Therefore, x = 7181/3427, y = 3307/3427

Hope it helps!

Answer 2

Dear Student,

Answer:x = 7181/3427
y = 3307/3427

Solution:

To solve such equations first add both equations then subtract,so that to simplify

$86x + 63y = 241 \\ \\ 63x + 86y = 215$
add both equations
$86x + 63y + 63x + 86y = 241 + 215 \\ \\ 149x + 149y = 456.......eq1$
subtract both equations

$86x - 63x + 63y - 86y = 26 \\ \\ 23x - 23y = 26 ......eq2$

substitute value of
$x = \frac{26 + 23y}{23}$
$149 \ \times \frac{26 + 23y}{23} + 149y = 456 \\ 3874 + 3427y + 3427y = 10488 \\ \\ 6854y = 6614 \\ y = \frac{6614}{6854} y = \frac{3307}{3427}$

put the value of y in eq 2

23 x -23(3307/3427) =26

23 x = 26+3307/149

23x= (3874+3307)/149

x = 7181/3427

Hope it helps you.