Question

Solve the following pair of linear equations graphically:

x+3y=6; x-3y=12.​

Answer 1

Given :-

pair of linear equations are

x+3y=6; x-3y=12.

To find:-

Solve the pair of linear equations graphically:

x+3y=6; x-3y=12.

Solution:-

See the given attachment for the solution.

Answer:-

Solution for the pair of linear equations=(9,-1)

Check:-

Given pair of linear equations

x+3y=6=>x+3y-6=0

a1=1;b1=3;c1=-6

and x-3y=12=>x-3y-12=0

a2=1;b2=-3;c2=-12

a1/a2=1/1=1

b1/b2=3/-3=-1

c1/c2=-6/-12=1/2

a1/a2≠b1/b2≠c1/c2

Given lines are consistent and independent or Intersecting lines with an unique solution.

x+3y=6----(1)

x-3y=12----(2)

(+)

__________

2x+0=18

_______

2x=18

=>x=18/2

=>x=9

On Substituting the value of x in (1) then

9+3y=6

=>3y=6-9

=>3y=-3

=>y=-3/3

=>y=-1

x=9 and y=-1

Solution =(9,-1)

We get same solutions from both graphical and algebraic methods