Question

please solve them the simultaneous linear equation
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Answer 1

ANSWER!

$\textsc{<strong>Linear </strong><strong>equations </strong><strong>in </strong><strong>two </strong><strong>variables</strong>}$

1. $\rm 97x + 53y = 177-->1$ $\rm 53x + 97y = 573-->2$

Add equations (1) and (2)

97x + 53y = 177

+ 53x + 97y = 573---> 2

150x +150y = 750

150 ( x + y ) = 750

x+y = $\frac{750}{150}$

x + y = 5 ----> 3

Now, subtract eqs. 1 and 2,

97x + 53y = + 177

- (53x + 97y = + 573)

.....-........-......... -.........

44x - 44y = - 396

(x - y) = $\frac{</strong><strong>-</strong><strong>396</strong><strong>}{</strong><strong>44</strong><strong>}$

x - y = -9 ---> 4

Now, subtract equations (3) and (4)

x + y = 5

- x - y = -9

..-......+........+

2y= 14

y = $\frac{</strong><strong>14</strong><strong>}{</strong><strong>2</strong><strong>}$

y = 7

Put y = 7 in equation (1)

97 x + 53 (7) = 177

97 x + 371 = 177

97 x = 177 - 371

97 x = - 194

x = $\frac{</strong><strong>-</strong><strong>194</strong><strong>}{</strong><strong>97</strong><strong>}$

x = -2

Solution: (x, y) =(-2,7)

Question 2 :

x + y = 5.5 ---> 1

x -y + 0.9 ---> 2

Add equations (1) and (2)

+ x + y = 5.5

+ (x - y = 0.9)

............................

2x = 6.4

x =$\frac{</strong><strong>6</strong><strong>.</strong><strong>4</strong><strong>}{</strong><strong>2</strong><strong>}$

x = 3.2

Put x = 3.2 in equation 1

3.2 + y = 5.5

y = 5.5 - 3.2

y = 2.3

Solutiond: (x, y) =(3.2,2.3)