So, I got this problem right but I did it different from the teacher. I just plugged in numbers. How do I solve this easier than that?
-x+3y=10
4x+y=25
Solve for x and y

- anonymous

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- amistre64

i take it this is a system of equation?

- amistre64

the 2nd equation is easier to "solve for y"

- amistre64

when you have "y" in terms of "x", you can use it in the 1st equation in the place of "y"... does that make sense?

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## More answers

- amistre64

y = -4x + 25 (from teh second equation)
-x + 3(-4x+25) = 10 (solve for x)

- amistre64

-x -12x +75 = 10
75-10 = x+12x
65 = 13x
65/13 = x .... if I did it right :)

- anonymous

i got x= 5/3 and y =6 1/4

- amistre64

x = 5 is a solid number, so we use that in our "equation for y" to determine the value of "y"
y = -4x +25
y = -4(5) +25
y = -20 + 25
y = 5
x = 5 ... i think :)

- amistre64

mit; whats your substitution for "y"; your y=equation?

- anonymous

amistre64 that is right. I answered it right I just didn't know how to solve it without plugging in numbers

- anonymous

Thanks

- amistre64

dian; does what I did make sense to you?

- anonymous

i isolate y in te second equation , then plugged tto the first eqution to solve for x

- amistre64

mit; what did you get for your y= equation?

- anonymous

Im off ; i got y= 25 /4x

- amistre64

mit; that would be in error
work it out step by step for me please

- anonymous

ok

- amistre64

4x+y=25 ... what do we do first?

- amistre64

we have "addition" involved; how do we get rid of a term that is held on by "addition"?

- anonymous

ok so yes that makes sense now. You isolated y then plugged that into the second equation to solve for x. It threw me off when I had two different letters to solve for.

- anonymous

4x + y=25
4x+y/4x=25/4x, so I plug it to the first equ.
-x +3(25/4x)=10

- amistre64

:) yes dian

- amistre64

Mit: you cant divide out of an addition problem.... you have to work it out with addition/subtraction. Hint: 4x-4x = 0 and y+0=y

- amistre64

4 + 6 = 10
6 does NOT equal 10/4 do you see that?
4 + 6 = 10
4-4 + 6 = 10 - 4
0 + 6 = 10 - 4
6 = 6

- anonymous

yeah I get it, so how do you solve it?

- amistre64

4x+y=25
we are stuck to the "y" by addition/subtraction. So, we need to get rid of that 4x thru addition/subtraction.
4x-4x +y = 25 - 4x you see what I did there?

- anonymous

yes

- amistre64

I look at it like this: if we are stuck by addition /subtraction ... we need to first get rid of the "neighbors". If anything is still stuck to the "y" it is going to be by multiplication/division... luckily, y is all by itself after we kick out the "neighbors".

- amistre64

so the value of "y" = 25 - 4x correct?

- anonymous

yes sir

- amistre64

good, now we "replace" this value of "y" in the other equation and solve that one for "x".
-x+3(25-x)=10 How do we solve this for "x"?

- anonymous

i get x = 10/ 87 , that s not right is it?

- anonymous

i dont know, which method do we choose

- amistre64

we have a few things to do first... remember what the "distributive" property tells us?
we know this:
3(10) = 30 right?
so, 3(6+4) should also equal 30...
the distributive property says we can do this:
3 (6+4)
3(6) + 3(4)
18 + 12 = 30 ... which is what we already know right?
Lets try it on this:
3(25 - x)
3(25) - 3(x) = 75 - 3x right?

- amistre64

-x + 75 - 3x = 10 we can add up our "x"s and kick the neighbor (75) out:
-x -3x +75-75 = 10 - 75
-4x = -65
you with me so far?

- anonymous

yeah

- amistre64

it would work out better if I kept track of my numbers lol...
3 (25-4x)
3(25) - 3(4x) = 75 - 12x...
-x -12x +75-75 = 10 -75
-13x = -65 .... this is were we should be at :)

- amistre64

when im wrong tell me :)

- anonymous

LOL, i was gunna point it out

- amistre64

now, we want that "x" all by itself but its got a leech, a spuse hanging on its side that we gotta get rid of.... this is a case for multiplication/division to get rid of the spouse..
-13x/13 = -65/ -13 remember that 2 negatives is a positive,,,
x = 65/13. this reduces to 5
5(13) = 65
x = 5

- amistre64

-13x/-13 of course is what i meant lol... my keyboard hates me :)

- amistre64

remember; 1st, get rid of the neighbors with addition/subtraction; 2nd, get rid of the spouse with multiplication/division... make sense?

- anonymous

OK Now I got it,,

- amistre64

since we have a solid nuber for x.. x=5... we use this in our "what does y equal" equation to get a solid value for "y"
"y" = 25 - 4x
y = 25 - 4(5)
y = 25 - 20
y = 5

- amistre64

we now know that y = 5 and x = 5 is the solution to this system of equations :) TADA!!!

- anonymous

cool beans

- amistre64

kick out the neighbors; then git rid of the spuse...... in that order! Gotta get to class now, Ciao :)

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