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?

i think there was a typo. you wrote pat brings 3 quarts of ice-cream to the party. each serving of ice-cream is 1 6 quart. how many total servings of ice-cream does pat bring to the party? i think the bold is supposed to be 1/6. so 1 quart of ice cream = 6 servings. 6 * 3 = 18.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1