Question

elimination method
5x/7+3y/7=1
x+2y/3=1

Answer 1

taym13, you keep on posting these elimination problems without ever replying to our questions. Do you want to learn, or are we your number-crunchers?

I'm willing to help you understand these problems.

Answer 2

yes i want to learn

Answer 3

Well, we hav\[\frac{5}{7}x+\frac{3}{7}y=1,\]\[x+\frac{2}{3}y=1.\]Our first step should be to eliminate one of the variables. Make your pick; it doesn't matter which one we do first.

Answer 4

x

Answer 5

Since we want to solve for x, we want to see just what do we need to do to both x's in both equations to make them equal to each other. Clearly, if we multiply the top equation by 7, we'll simplify the expression. Similarly, if we multiply the bottom equation by -5, we'll be able to eliminate x:\[\frac{5}{7}x+\frac{3}{7}y=1,\]we multiply by 7:\[5x+3y=7.\]Now, we multiply the bottom equation by -5:\[-5x-\frac{10}{3}y=-5.\]Are you with me thus far?

Answer 6

yes, i am

Answer 7

Now, can you add these two equations and tell me what you get?

Answer 8

That is,

5x + 3y = 7
-5x - (10/3)y = -5
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? = ?