Question : Number of solution of the two equations 4x – y = 2 and 2y – 8x + 4 = 0 is:
Option 1: Zero
Option 2: one
Option 3: two
Option 4: Infinitely many
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Correct Answer: Infinitely many
Solution : Given: $4x - y = 2$-----(equation 1) and $2y - 8x + 4 = 0$-----(equation 2) There are an infinite number of possible solutions for the equation system if two lines are in the same precise line if they share the same slope and y-intercept. Rearranging equation (1) we get, $y = 4x - 2$ Rearranging equation (2) we get, $2y = 8x - 4$ $⇒y = 4x - 2$ From the above equation, we can see that both lines are the same. So, there will be infinitely many solutions. Hence, the correct answer is infinitely many.
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