anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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amistre64
  • amistre64
i take it this is a system of equation?
amistre64
  • amistre64
the 2nd equation is easier to "solve for y"
amistre64
  • 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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amistre64
  • amistre64
y = -4x + 25 (from teh second equation) -x + 3(-4x+25) = 10 (solve for x)
amistre64
  • amistre64
-x -12x +75 = 10 75-10 = x+12x 65 = 13x 65/13 = x .... if I did it right :)
anonymous
  • anonymous
i got x= 5/3 and y =6 1/4
amistre64
  • 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
  • amistre64
mit; whats your substitution for "y"; your y=equation?
anonymous
  • anonymous
amistre64 that is right. I answered it right I just didn't know how to solve it without plugging in numbers
anonymous
  • anonymous
Thanks
amistre64
  • amistre64
dian; does what I did make sense to you?
anonymous
  • anonymous
i isolate y in te second equation , then plugged tto the first eqution to solve for x
amistre64
  • amistre64
mit; what did you get for your y= equation?
anonymous
  • anonymous
Im off ; i got y= 25 /4x
amistre64
  • amistre64
mit; that would be in error work it out step by step for me please
anonymous
  • anonymous
ok
amistre64
  • amistre64
4x+y=25 ... what do we do first?
amistre64
  • amistre64
we have "addition" involved; how do we get rid of a term that is held on by "addition"?
anonymous
  • 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
  • anonymous
4x + y=25 4x+y/4x=25/4x, so I plug it to the first equ. -x +3(25/4x)=10
amistre64
  • amistre64
:) yes dian
amistre64
  • 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
  • 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
  • anonymous
yeah I get it, so how do you solve it?
amistre64
  • 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
  • anonymous
yes
amistre64
  • 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
  • amistre64
so the value of "y" = 25 - 4x correct?
anonymous
  • anonymous
yes sir
amistre64
  • 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
  • anonymous
i get x = 10/ 87 , that s not right is it?
anonymous
  • anonymous
i dont know, which method do we choose
amistre64
  • 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
  • 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
  • anonymous
yeah
amistre64
  • 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
  • amistre64
when im wrong tell me :)
anonymous
  • anonymous
LOL, i was gunna point it out
amistre64
  • 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
  • amistre64
-13x/-13 of course is what i meant lol... my keyboard hates me :)
amistre64
  • amistre64
remember; 1st, get rid of the neighbors with addition/subtraction; 2nd, get rid of the spouse with multiplication/division... make sense?
anonymous
  • anonymous
OK Now I got it,,
amistre64
  • 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
  • amistre64
we now know that y = 5 and x = 5 is the solution to this system of equations :) TADA!!!
anonymous
  • anonymous
cool beans
amistre64
  • amistre64
kick out the neighbors; then git rid of the spuse...... in that order! Gotta get to class now, Ciao :)

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