1. Lisa is working with the system of equations x + 2y = 7 and 2x - 5y = 5. She multiplies the first equation by 2 and then subtracts the second equation to find 9y = 9, telling her that y = 1. Lisa then finds that x = 5. Thinking about this procedure, Lisa wonders:

There are lots of ways I could go about solving this problem. I could add 5 times the first equation and twice the second or I could multiply the first equation by - 2 and add the second. I seem to find that there is only one solution to the two equations but I wonder if I will get the same solution if I use a different method?

What is the answer to Lisa's question? Explain.

2. Does the answer to the first question change if we have a system of two equations in two unknowns with no solutions? What if there are infinitely many solutions?

Question

5 October, 02:55

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Mckayla Norris · Answer 1

All methods are supposed to be correct in most if not all situations and it should not matter if you use a different method given the options