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?