Question

The value of k so that the system of equations 3x-y-5=0and 6x-2y-k=0have infinitely many solutions is

Answer 1

Answer:

infinitely many solutions.

Answer 2

Answer:

k = 10

Step-by-step explanation:

System of equations

y = $m_{1}$ x + $b_{1}$

y = $m_{2}$ x + $b_{2}$

has infinitely many solutions if $m_{1}$ = $m_{2}$ and $b_{1}$ = $b_{2}$

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Solve 3x - y - 5 = 0 and 6x - 2y - k = 0 for "y"

3x - y - 5 = 0 ⇒ y = 3x - 5

6x - 2y - k = 0

2y = 6x - k ⇒ y = 3x - $\frac{k}{2}$

$\frac{k}{2}$ = 5 ⇒ k = 10