The system of pair of equations 4x−3y+12=0 and 2x+3y−15=0 has
a unique solution
Given equations: 4x−3y+12=0 and 2x+3y−15=0
On comparing with the a1x+b1y+c1=0 and a2x+b2y+c2=0, we get
a1=4, b1=−3, c1=12
a2=2, b2=3, c2=−15
Here,
a1a2=42=2 and b1b2=−33=−1
⇒a1a2 ≠ b1b2
We know that when a pair of linear equations in two variables a1x+b1y+c1=0 and a2x+b2y+c2=0, have
⇒a1a2 ≠ b1b2
then the lines representing these equations will intersect and have a unique solution.
Therefore, the given pair of equations has a unique solution.