algebra.. solving systems..?

Question

x+y=1
&
y=x-3

Answer 1

x=2, y= -1

first change to
x+y=1
x-y=3
add straight down

Answer 2

i got it =D - you can use elimination, which is what I did
x = 2
y = -1
first you move it so the variables and numbers are on separate sides
x+y = 1 --> x+y = 1
y = x-3 --> y-x = -3
second, you can move it so x and y aligns...makes it easier to solve
x+y = 1 --> y+x = 1
y-x = -3 --> y-x = -3
3rd, since this is a simple system of equations, you can use elimination to solve in which case u can eliminate x or y, i choose y, and you can do so by multiplying -1 to the first equation
-1(y+x = 1) --> -y-x = -1
y-x = -3 --> y-x = -3
4th, the y's cancel so you are left with x only
-2x = -4
5th, you solve for x, which unless you are really dumb, i don't need to show you, but x = 2
6th, with x found, plug it into any of the ORIGINAL equations and solve for y, in which case i chose the 1st one
x+y = 1
(2)+y = 1
y = -1

and there is your solution
x = 2
y = -1

BTW - you can also use substitution, since the y is given as the 2nd equation, simply replace the "y" in the first equation with the second equation, which is what the person above me used

Answer 3

since you have y=somthing you plug in what is happening on the other side of the y into the other equation
y=x-3
x+y=1 (substitute x-3 for y)

x+x-3=1 (add factors together)
2x-3=1 (add 3 to both sides)
2x=4 (divide both sides by 2)
x=2
plug x=2 into one of the following equations:
y= x-3
y=2-3
y= -1
or
x+y=1
2+y=1 (subtract 2 from both sides)
y= -1

x=2, y= -1

Answer 4

x + y = 1 and y = (x - 3) so..

x + (x-3) = 1 so...
2x - 3 = 1 so...
2x -3 + 3 = 1 + 3
2x = 4 so...
2x/2 = 4/2 equals
x = 2

now check your answer by putting x = 2 into the first equation...
2 + y = 1
remember y = x -3 so...
2 + (2-3) = 1
2 + (-1) = 1
1 = 1
Ok, it checks out.

Answer 5

since the second equation is solved for y, you can substitute x - 3 in for y in the first equation
x + (x - 3) = 1
2x - 3 = 1
2x = 4
x = 2
plugging that answer back in,
2 + y = 1
y = -1

Answer 6

substitute y = x - 3 into the first equation for y

x + (x - 3) = 1
2x - 3 = 1
2x = 4
x=2

sub it back into the second equation:

y = x - 3
=2 - 3
=-1

Answer 7

y=x-3, which we can substitute for y in the first equation...

x+(x-3)=1

now, combine like terms

2x-3=1

solve for x

2x=4
x=2

Now that we know x=2, we can plug that into either equation to find y.

2+y=1

slve the equation for y

y=-1