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

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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

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

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