Question

17x + 23y = 40 and 23x + 17y = 80. find x + y. a) 120. b) 40 c) 3. d) 80

Answer 1

Answer:

Option c - 3

Step-by-step explanation:

Given : Equation $17x + 23y = 40$ and  $23x + 17y = 80$

To find : The value of $x+y$ ?

Solution :

Let $17x + 23y = 40$ .....(1)

Let $23x + 17y = 80$ ....(2)

Multiply (1) by 23 and (2) by 17 to eliminate x,

$391x +529y =920$ .....(3)

$391x +289y =1360$ .....(4)

Subtract (3) and (4),

$391x +529y-(391x +289y)=920-1360$

$240y=-440$

$y=-\frac{440}{240}$

$y=-\frac{11}{6}$

Substitute in (1),

$17x + 23(-\frac{11}{6})= 40$

$17x-\frac{253}{6}= 40$

$17x= 40+\frac{253}{6}$

$17x=\frac{493}{6}$

$x=\frac{493}{102}$

Substitute the value of x and y in the expression,

$x+y=\frac{493}{102}+(-\frac{11}{6})$

$x+y=\frac{493}{102}-\frac{11}{6}$

$x+y=\frac{2958-1122}{612}$

$x+y=\frac{1836}{612}$

$x+y=3$

Therefore, The value is $x+y=3$

So, Option c is correct.

Answer 2

Answer:

c=3

steps of explaining:-

17x+23y=40 ( 1)

23x+17y=80 (2)

by eliminate method,

multiple (1) by 23 and (2)by 17

23(17x+23y=40)

391x+529y=920 (3)

17 ( 23x+17y=80)

391x+289y=1360(4)

substrate eq 3 and 4

+391x+529y=920

- 391x+289y=1360

240y=-440

y=-440/240

y =-11/6

by eq 1

17x+23y=40

17x-253/6=40

17x= 40+253/6

17x=40×7 +253/3

17x=240+253/6

17×6(x) =493/6

102x=493

x=493/102

now x+y=493/102 + (-11/6)

=2958-1122/612

=1836/612= 3

therefore x+y =3