SAT Exam > SAT Questions > kx − 3y = 44x − 5y = 7In the syst...
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kx − 3y = 4
4x − 5y = 7
In the system of equations above, k is a constant and x and y are variables. For what value of k will the system of equations have no solution?
4x − 5y = 7
In the system of equations above, k is a constant and x and y are variables. For what value of k will the system of equations have no solution?
- a)12/5
- b)16/7
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
kx − 3y = 44x − 5y = 7In the system of equations above, k ...
Choice A is correct. If a system of two linear equations has no solution, then the lines represented by the equations in the coordinate plane are parallel. The equation kx − 3y = 4 can be rewritten as y =
where k/3 is the slope of the line, and the equation 4x − 5y = 7 can be rewritten as y =
where 4/5 is the slope of the line. If two lines are parallel, then the slopes of the line are equal. Therefore, 4/5 = k/3, or k = 12/5. (Since the y-intercepts of the lines represented by the equations are 
and 
the lines are parallel, not identical.)
Choices B, C, and D are incorrect and may be the result of a computational error when rewriting the equations or solving the equation representing the equality of the slopes for k.
where k/3 is the slope of the line, and the equation 4x − 5y = 7 can be rewritten as y = where 4/5 is the slope of the line. If two lines are parallel, then the slopes of the line are equal. Therefore, 4/5 = k/3, or k = 12/5. (Since the y-intercepts of the lines represented by the equations are and the lines are parallel, not identical.)Choices B, C, and D are incorrect and may be the result of a computational error when rewriting the equations or solving the equation representing the equality of the slopes for k.
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kx − 3y = 44x − 5y = 7In the system of equations above, k is a constant and x and y are variables. For what value of k will the system of equations have no solution?a)12/5b)16/7c)d)Correct answer is option 'A'. Can you explain this answer?
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