Question

Check whether the pair of equations x + 3y = 6, 2x - 3y = 12 is consistent.​

Answer 1

Answer:

Yes; x=6,y=0

Step-by-step explanation:

The given pair can be written as

x+3y−6=0 and 2x−3y−12=0

Here a^1 =1,b1=3,c^1=-6 ..( eq 1 )

and a^2=2,b^2=-3,c^2=-12..(eq2)

so a^1/a^2=1/2,b^1/b^2=3/-6=1/-2

Hence a^1/a^2  b^1/b^2,

Thus the given pair of equation is consistent.

To solve them graphically we have

Consider x+3y−6=0

x=0⟹y=2

x=3⟹y=1

Join the points by drawing line.

Consider 2x−3y−12=0

x=0⟹y=−4

x=3⟹y=−2

Join the two points by drawing line.

The given pair of linear equation has unique solution x=6 and y=0.