Match the following:
A.y=−32−x2;x=−3−2y(i)Inconsistent pairB.5x=6−3y;9y=12−15x(ii)Dependent pairC.y=27−x7;y=185−x5(iii)Unique solution
A-ii, B-i, C-iii
Write each of the pairs of equations in the standard form where
a1x+b1y+c1=0
a2x+b2y+c2=0
Inconsistent pair: a1a2=b1b2≠c1c2
Dependent pair: a1a2=b1b2=c1c2
Unique solution:a1a2≠b1b2
A.y=−32−x2⇒x2+y+32=0x=−3−2y⇒x+2y+3=0Here a1a2=12,b1b2=12,c1c2=12
Hence,a1a2=b1b2=c1c2. Thus, it is a dependent pair.
B. 5x=6−3y⇒5x+3y−6=0
9y=12−15x⇒15x+9y−12=0
Here a1a2=13,b1b2=13,c1c2=12
Hence,a1a2=b1b2≠c1c2. Thus, it is an inconsistent pair.
C. y=27−x7⇒x7+y−27=0
y=185−x5⇒x5+y−185=0
Here a1a2=16,b1b2=57
Hence, a1a2≠b1b2. Thus, it is a consistent pair.