Find the value of k for which the system of equations has a unique solution:
4x -5y = k, 2x -3y = 12
(step by step)
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Answer:
k not equal to 20 answer
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4x-5y=k, 2x-3y=12.
4x-5y-k=0.
2x-3y-12=0.
a1=4. a2=2.
b1=-5. b2=-3.
c1=-k. c2=-12.
a1/a2=4/2=2.
b1/b2=-5/-3=5/3.
c1/c2=-k/-12=k/12.
4/2=k/12.
2k=4×12.
2k=48.
k=48/2.
k=24.
c1/c2=24/12=2.
a1/a2≠b1/b2.
So, the system of equation has a unique solution.
I think this is your answer.
5/3=k/12.
3k=5×12.
3k=60.
k=60/3.
k=20.
c1/c2=20/12=5/3.
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