subsitution, elimination, and foil

[HispanicIcePrincess]

Hello! I was just wondering, when using the elimination method (multiplication/division), do you add when the signs are the same or different? For instance, in the problem,

3x+8y=1
7x+4y=17,

after multiplying the top equation by seven and the bottom one by three to get

21x+56y=7
21x+12y=51

subtraction rather than addition is used, being that the two twenty-ones share the same sign, right?

Is (3,-1) the correct answer for this problem?

I'm sorry for bombarding you with so many questions and such inconvenience, but I'd greatly appreciate it if I received an accurate reply to my inquiries by tomorrow night. The earlier the better, but don't stress on it too much. It's just that I have to take my math final on Thursday =( Therefore, it would be highly appreciated to have an answer as soon as possible =) Well, thanks for your cooperation. I'm looking forward to hearing from you!

 

[jonboy]

There's an easier way. Your way uses big numbers. Smaller the number it's the easier right (unless fractions) ?

...3x + 8y = 1 [1]
...7x + 4y = 17 [2]

Multiply [2] by 2, name it [3]:

...14x + 8y = 34 [3]
...3x + 8y = 1 [1]

Subtract like terms in [3] and [1]: 14x - 3x + 8y - 8y = 34 - 1

...11x = 33

...x = 3

Plus x in to solve for y:...3(3) + 8y = 1

...9 + 8y = 1

...y = -1

So you are correct! Great work!

 

[jwpaine]

Check by plugging in your answer of x and y into both equations. IF the equations are true, than your answer is correct.