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Solution



Given
In this question, we are given that
    • Two simultaneous equations: 2x + 6y = 7 and x – my = -2

To find
We need to determine
    • The value of m for which the given equations will have no solution

Approach and Working out
The equations will have no solution if the ratio of the coefficients of the variables will not be equal to the ratio of the constant terms
    • Hence, 2/1 = 6/-m
    Or, m = -6/2 = -3

Thus, option B is the correct answer.

Correct Answer: Option B
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[quote="sjuniv32"] 2x+6y = 7
x-my = -2
For which of the following values of m will the system equations above have no solution?

(A) -6

(B) -3

(C) 0

(d) 3

(E) 6



[b]Can it be solved in some other ways?
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Russ19

sjuniv32
2x+6y = 7
x-my = -2
For which of the following values of m will the system equations above have no solution?

(A) -6

(B) -3

(C) 0

(d) 3

(E) 6



[b]Can it be solved in some other ways?
[/b]
Here's an alternate approach:

\(­2x + 6y = 7\) --- (1)
\(x - my = -2\)  --- (2)

Multiply eq 2 by 2 and subtract from eq 1:

\(6y + 2my = 11\)
\(2y (3 + m) = 11\)

\(m = -3\) would make it  \(0 = 11\), which is not possible. Also, remember y can be a fraction (like \(\frac{11}{2}\)), so we can keep adjusting the value of y for m as long as \(m ≠ -3\)
 ­
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