solve by elemination

{x + y = 10
x - y = 2
solve by substitution

y = x +1
2x + y = 7



:eek:

-------IGNORE THE DOTS, I USED IT FOR PROPER SPACING------
For elimination, simply add the two equations.
x + y = 10
x - y = 2
_________
2x... = 12
2x/2.. = 12/2
... x=6

Choose one of the equation to solve for (y) and plug 6 instead of an (x).
6 + y = 10
-6... -6
__________
... y = 4
Your answer should look like this: (6,4)-- this is where the two lines intersect.


For substitution, plug y= x + 1 into the second equation 2x + y = 7.
2x + (x+1) = 7
2x + x + 1 = 7
3x + 1 = 7
... - 1... -1
_____________
3x... = 6
3x/3... = 6/3
... x = 2 ------- now choose one of the equation (any one of the two), and use (2) instead of an (x).

let us use y = x + 1
y = 2 + 1
y = 3 ----- this is your (y)

your answer is (2,3)

A lot of help !

Exampls of elimination by substitution

x+y=7

exampls of elimination by substitution

Pick any two independent equations.

X = Y + 45
Y = 49

They're usually more complicated that this, but this serves the purpose.

Substitute "49" everywhere you see "Y"

X = 49 + 45

You then solve for X. That's substitution.

x+y=10
x-y=2

2x=12
x=6

6+y=10
y=4
(6,4)


y=x-1
2x+y=7

2x+x+1=7
3x+1=7
3x=6
x=2

2(2)+y=7
4+y=7
y=3
(2,3)

x+y+0
x+y+4

elimination:
x+y=10 x+y=10 x+y=10
x-y=2 -(x+y=2)- -x+y=-2

2y=10-2
2y=8/2
y=4
subtitution:
y=x+1 2x+(x+1)=7
2x+y7 (2x+x)+(1=7) 3x=7-1 3x=6/3 x=2
2x+y=7