How do solve the following linear system?: -7x + y = -19 , x - 3y = -6 ?

1 Answer
Mar 31, 2018

Hence, the values of x and y are
(x,y)-=(63/20,61/20)

Explanation:

-7x+y=-19.........(1)

x-3y=-6..........(2)

Eliminating x from (2)

x=3y-6

Substituting for x in (1)

-7x+y=-19

-7(3y-6)+y=-19

-7xx3y+7xx6+y=-19

-21y+42+y=-19

(-21y+y)=-19-42

-20y=-61

y=61/20

x=3y-6

x=3xx61/20-6

x=(3xx61)/20-(6xx20)/20

x=(183-120)/20

x=63/20

Checking,,

-7x+y=-19

lhs=
-7x+y=
-7xx63/20+61/20
=(-7xx63+61)/20
=(-441+61)/20
=-380/20
=-19
=rhs

x-3y=-6

lhs=
x-3y=
63/20-3xx61/20

=(63-3xx61)/20

(63-183)/20

-120/20

=-6

=rhs

Hence, the values of x and y are
(x,y)-=(63/20,61/20)