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How many solutions will each system of linear equation have?

How many solutions will each system of linear equation have?-example-1

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Answer:

The top system of equations has one solution, the middle system has infinitely many, and the bottom system has no solution.

Explanation:

We can immediately see the top system has one solution because the two equations have different slopes.

For the middle system, we can rearrange terms and multiply by 3 to get that the equations are the same line, so there are infinitely many solutions.

Finally, we can move the -2x to the other side in the first equation of the bottom system to get 2x+y=5. But it also equals -7 from the second equation! This is impossible, so there are no solutions to the bottom system.

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