Kaplan SAT Prep Plus Math Question?

Question

#{5x-3y=10#
#{6y=kx-42#

(No idea how to put them in the same curly bracket)

Why does #k/2# equal to #5#, the coefficient of #y# in the first equation?

In the system of linear equations above, k represents a constant. If the system of equations has no solution, what is the value of 2k?

Answer: #2k = 20#

Thanks in advance!

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Answer 1 · 2018-06-04T05:06:48

# k=10#.

Suppose that the System of Linear Equations is,

#a_1x+b_1y+c_1=0 and a_2x+b_2y+c_2=0#.

This system has no solution iff #a_1b_2-a_2b_1=0#.

We have, #a_1=5, b_1=-3, a_2=k and b_2=-6#.

#:. a_1b_2-a_2b_1=0 rArr 5(-6)-k(-3)=0#.

#:. k=10#.