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How do you know when an equation has an infinite amount of solutions or no solution?

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Solve by using three equations and variables. I have 30 coins, all nickels, dimes, and quarters, worth $4.60. There are two more dimes than quarters. How many of each kind of coin do I have?

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A car and a bike set out at noon from the same point headed in the same direction. At 1:00 P.M., the car is 60 km ahead of the bike. Find how fast each travels, given that the car travels four times as fast as the bike.

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