Question

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

Answer 1

i take it this is a system of equation?

Answer 2

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

Answer 3

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?

Answer 4

y = -4x + 25 (from teh second equation)

-x + 3(-4x+25) = 10 (solve for x)

Answer 5

-x -12x +75 = 10

75-10 = x+12x

65 = 13x

65/13 = x .... if I did it right :)

Answer 6

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

Answer 7

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 :)

Answer 8

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

Answer 9

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

Answer 10

Thanks

Answer 11

dian; does what I did make sense to you?

Answer 12

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

Answer 13

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

Answer 14

Im off ; i got y= 25 /4x

Answer 15

mit; that would be in error

work it out step by step for me please

Answer 16

ok

Answer 17

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

Answer 18

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

Answer 19

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.

Answer 20

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

Answer 21

:) yes dian

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

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?

Answer 26

yes

Answer 27

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".

Answer 28

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

Answer 29

yes sir

Answer 30

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"?

Answer 31

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

Answer 32

i dont know, which method do we choose

Answer 33

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?

Answer 34

-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?

Answer 35

yeah

Answer 36

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 :)

Answer 37

when im wrong tell me :)

Answer 38

LOL, i was gunna point it out

Answer 39

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

Answer 40

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

Answer 41

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

Answer 42

OK Now I got it,,

Answer 43

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

Answer 44

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

Answer 45

cool beans

Answer 46

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