Question

Systems of equations. 4x+3y=5, 2x-5y=-17?

Answer 1

If you subtract 2 times the second equation from the first you will get an equation you can solve for y.

Answer 2

Does that make sense or do you need further clarification?

Answer 3

No, that makes sense. Thankyou.(:

Answer 4

Wait, no it doesnt.. Im confused. Subtract what ?

Answer 5

there are a few ways to solve systems of equation; one way was by substitution which can be rather labor intensive; the other method is called elimination, and that is what polpak suggests

Answer 6

Okay... How do you eliminate?

Answer 7

4x+3y=5
2x-5y=-17 <-- if we multiply this equation by -2 we get these results


4x+ 3y = 5
-4x+10y =34 now when we add these together, the x parts cancel out
------------
0 +13y = 39 ; now we solve for y by dividing out the 13 to get:

y = 39/13

Answer 8

we can do the same thing to eliminate the y parts first, but it takes modifying both equations to do so; but still might be worth it to avoid dealing with fractions :)

Answer 9

I ... how... blah. I need to do this in fractional form. How do you do that?

Answer 10

Fractional form? I think that just means leave it as 39/13 instead of writing out the decimal answers.

Answer 11

But what about x? Thats only the answer for y, rght?

Answer 12

:)

4x +3y =5 <-- multiply by 5
2x -5y =-17 <-- multiply by 3

20x +15y =25
6x -15y =-51 ; now add them together
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26x + 0 = -26 ; divide out the 26 to get:

x = -26/26 = -1 ... if i did it right :)

Answer 13

... I hate math. :l Why do you multiply the whole equation?

Answer 14

Once you get an answer for y you can plug it into either equation to find x.

Answer 15

You multiply the whole equation because you want to get the coefficients ( numbers in front of the variables) to match. In order to do something to one side of the equation (multiply by 3 for example) you must do the same thing to the other side so they will stay equal.

Answer 16

to dbl check lets use these in the equations and solve

4x+3y=5
4(-1) + 3(39/13) = 5(13)/13
-4(13/13) + 117/13 = 65/13
117 - 52 = 65 .... its good there

2x-5y=-17
2(-1)-5(39/13)=-17(13)/13
-2(13)/13 -195/13 = -221/13
-26-195 = -221 .... and its good

Answer 17

If I tell you that
5x + 3y = 17

Then 5 times 5x + 3y must equal 5 times 17.

Answer 18

equations can change form while they keep the same value

so what we want to do is change the form into something we can use

Answer 19

... Okay. Hold on, let me work this all out and see if i get confused.

Answer 20

:) i almost got confused on this one lol alot of fractional work to keep track of

Answer 21

Certainly. What you're trying to do is find something you can multiply one (or both) of the equations by so that when you add the equations together you make one of the variables have a 0 for a coefficient.

Answer 22

Alright! I did it and it all made sense and i got the same answers you guys did. (: Thank you.