Question

Solve the following system of equations. 217x +131y =913 ,131x + 217y = 827

Answer 1

Answer:-

Step by step explanation:-

217x+131y=913.....(equation 1)

131x+217y=827.....(equation 2)

add equation (1) and (2)

348x+348y=1,740

348 (x+y)=1,740

x+y= 1,740/348

x+y=5.....(equation 3)

subtract equation (2) from (1)

217x+131y=913

131x+217y=827

(-)__(-)____(-)________

86x-86y=86

86(x-y)=86

x-y = 86/86

x-y=1.....(equation 4)

add equation (3) and (4)

x+y=5

x-y=1

___________

2x=6

x=6/2

x=3

substituting the value of x in equation 3

x+y=5

3+y=5

y=5-3

y=2

result :- x=3,y=2 is the solution of given equation

Answer 2

Answer

$\sf \dashrightarrow 217x + 131y = 913 \: \: --- (i)$

$\sf \dashrightarrow 131x + 217y = 827 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow 217x + 131y = 913$

$\sf \dashrightarrow 217x = 913 - 131y$

$\sf \dashrightarrow x = \dfrac{913 - 131y}{217}$

Now, let's find the value of y by second equation.

$\sf \dashrightarrow 131x + 217y = 827$

$\sf \dashrightarrow 131 \bigg( \dfrac{913 - 131y}{217} \bigg) + 217y = 827$

$\sf \dashrightarrow \dfrac{119603 - 17161y}{217} + 217y = 827$

$\sf \dashrightarrow \dfrac{119603 - 17161y + 47089y}{217} = 827$

$\sf \dashrightarrow \dfrac{119603 + 29928y}{217} = 827$

$\sf \dashrightarrow 119603 + 29928y = 827 \times 217$

$\sf \dashrightarrow 119603 + 29928y = 179459$

$\sf \dashrightarrow 29928y = 179459 - 119603$

$\sf \dashrightarrow 29928y = 59856$

$\sf \dashrightarrow y = \dfrac{59856}{29928}$

$\sf \dashrightarrow y = 2$

Now, let's find the value of x by first equation.

$\sf \dashrightarrow 217x + 131y = 913$

$\sf \dashrightarrow 217x + 131(2) = 913$

$\sf \dashrightarrow 217x + 262 = 913$

$\sf \dashrightarrow 217x = 913 - 262$

$\sf \dashrightarrow 217x = 651$

$\sf \dashrightarrow x = \dfrac{651}{217}$

$\sf \dashrightarrow x = 3$

Hence, the values of x and y are 3 and 2 respectively.