Question

.Solve for x and y 47x+31y=63, 31x+47y=15

Answer 1

Add equation 1&2

47x+31y=63; 31x+47y=15

78x+78y=78 now divide by 78 each side

x+y= 1 ......... equation (3)

now subtract equation 1&2

47x+31y=63; 31x+47y=15

16x-16y= 48 now divide by 16 each side

x-y = 3 ............. equation (4)

solve equations 3&4

x = 2 , y= -1

Answer 2

$\large\underline\pink{Given:-}$

• 47x + 31y = 63
• 31x + 47y = 15

$\large\underline\pink{To find:-}$

• Fine the value of x and y ....?

$\large\underline\pink{Solutions:-}$

47x + 31y = 63 ______(i)

31x + 47y = 15 ______(ii)

multiplying Eq. (i) by 31 and Eq. (ii) by 47, we get.

1457x + 961y = 1953 ________(iii)

1457x + 2209y = 704 _________(iv)

Subtracting Eq. (iii) from Eq. (iv).

${1457x} \: + \: {961y} \: \: = \: \: {1953} \\ {1457x} \: + \: {2209y} \: \: = \: \: {704} \\ \underline{ \: \: \: \: \: \: \: \: \: - \: \: \: \: \: \: \: \: \: \: \: \: \: - \: \: \: \: \: \: \: \: \: \: \: \: \: = \: \: \: \: \: - \: \: \: \: \: \: \: \: \: \: \: } \\ \: \: \: \: \: \: \: \: \: \: \: {-1248} \: \: \: \: \: = \: \: \: {1248}$

$\: \: \: \: \: \leadsto \: \: y \: \: = \: \: {-1}$

Now, putting the value y in Eq. (i)

47x + 31y = 63

47x + 31(-1) = 63

47x - 31 = 63

47x = 63 + 31

47x = 94

x = 94/47

x = 2

hence, the value of x is 2 and y is -1.