Mathematics, 14.02.2020 04:04 stinematesa

Beyonce is solving a system of equations:
2x-3y=-2 and 4x+y=24
She multiplies the second equation by 3 and then adds the first equation to find 14x=-70, showing her that x=5. Beyonce finds that y=4. Thinking about this process, Beyonce says out loud,
“There are lots of ways I could go about solving this problem. I could do the method above 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 Beyonce's question? Be sure to show work or explain reasoning.

Is the answer to (a) different if we have a system of two equations with no solutions? What if there are infinite solutions?

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Beyonce is solving a system of equations:
2x-3y=-2 and 4x+y=24
She multiplies the second...