For what value of k does the system below have infinitely many solutions? 5x - 2y = 12 kx - 6y = 36
Step-by-step solution
For infinitely many solutions, the second equation must be a multiple of the first. Since -6y is -2y \times 3, multiply the whole first equation by 3: 15x - 6y = 36. So k = 15.
Common mistake
Matching only the y-coefficients without multiplying the whole equation, or picking a value that makes the system have no solution.
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What is the answer to For what value of k does the system below have infinitely many solutions? 5x - 2y = 12 kx - 6y = 36
Answer: C) 15. For infinitely many solutions, the second equation must be a multiple of the first. Since -6y is -2y \times 3, multiply the whole first equation by 3: 15x - 6y = 36. So k = 15.
How do you solve it?
For infinitely many solutions, the second equation must be a multiple of the first. Since -6y is -2y \times 3, multiply the whole first equation by 3: 15x - 6y = 36. So k = 15.
What mistake do most students make?
Matching only the y-coefficients without multiplying the whole equation, or picking a value that makes the system have no solution.
What SAT topic is this?
Algebra. Practice more free Algebra questions with instant feedback at Syntene Learn.