Question

solve the following pair of linear equation by the substitution method​

Answer 1

(x+y-8)/2……….(1)

(x+2y-14)/3………(2)

(3x+y-12)/11……..(3)

Take eq 1& 2

(x+y-8)/2= (x+2y-14)/3

3(x+y-8)= 2(x+2y-14)

3x+3y-24= 2x+4y-28

3x-2x+3y-4y= -28+24

x-y= -4

x-y+4=0…………….(3)

Take eq 2 & 3

(x+2y-14)/3 = (3x+y-12)/11

11 (x+2y-14)= 3(3x+y-12)

11x+22y - 154= 9x+3y-36

11x -9x+22y-3y= -36+154

2x+19y= 118

2x+19y-118=0…………….(4)

Multiply equation (3) by 2  

2x-2y+8=0………..(5)

subtract equation (4) from eq (5)

2x-2y+8=0

2x+19y-118=0

(-)   (-)   (+)

_______________

-21y+126=0

-21y=-126

y= 126/21= 6

y= 6

From eq 3

x+y -8=0

x+6-8=0

x-2=0

x=2

Hence, the value of x= 2 & y= 6