SOLUTION: Solve each system by the addition method. x + y = 7 X – y = 9 x – y = 12 2x + y = 3 2x – y = -5 3x + 2y = 3 3x + 4y = -5 5x + 6y = -7

Algebra ->  College  -> Linear Algebra -> SOLUTION: Solve each system by the addition method. x + y = 7 X – y = 9 x – y = 12 2x + y = 3 2x – y = -5 3x + 2y = 3 3x + 4y = -5 5x + 6y = -7      Log On


   

Question 167817: Solve each system by the addition method.
x + y = 7
X – y = 9




x – y = 12
2x + y = 3




2x – y = -5
3x + 2y = 3






3x + 4y = -5
5x + 6y = -7
Found 2 solutions by nerdybill, checkley77:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
#1
Adding the two equations together:
x + y = 7
X – y = 9
---------
2x = 16
dividing both sides by 2:
x = 8
.
substituting the above into:
x + y = 7
8 + y = 7
y = -1
.
solution:
x = 8
y = -1
.
.
.
#2
Add the two equation together:
x – y = 12
2x + y = 3
-----------
3x = 15
x = 5
.
substitute the above into:
x – y = 12
5 – y = 12
- y = 7
y = -7
.
solution:
x = 5
y = -7
.
.
.
#3
2x – y = -5
3x + 2y = 3
Multiply both sides of equation 1 by 2 THEN add:
4x – 2y = -10
3x + 2y = 3
-------------
7x = -7
x = -1
.
substitute the above into:
2x – y = -5
2(-1) – y = -5
-2 - y = -5
- y = -3
y = 3
.
solution:
x = -1
y = 3
.
.
.
#4
3x + 4y = -5
5x + 6y = -7
Multiply 1st equation -5, 2nd equation by 3, then add:
-15x - 20y = 25
15x + 18y = -21
-----------------
- 2y = 4
y = -2
.
substitute the above into:
3x + 4y = -5
3x + 4(-2) = -5
3x - 8 = -5
3x = 3
x = 1
.
solution:
x = 1
y = -2

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
x+y=7
x–y=9 add
-------------
2x=16
x=16/2
x=8 ans.
8+y=7
y=7-8
y=-1 ans.
*************************
x–y=12
2x+y=3 add
-------------------
3x=15
x=15/3
x=5 ans.
5-y=12
-y=12-5
-y=7
y=-7 ans.
***********************************
2x–y=-5 multiply this equation by 2 & add.
3x+2y=3
4x-2y=-10
-----------
7x=-7
x=-7/7
x=-1 ans.
2*-1-y=-5
-2-y=-5
-y=-5+2
-y=-3
y=3 ans.
*************************
3x+4y=-5 multiply by 5
5x+6y=-7 multiply by -3 & add.
15x+20y=-25
-15x-18y=21
------------------
2y=-4
y=-4/2
y=-2 ans.
3x+4*-2=-5
3x-8=-5
3x=-5+8
3x=3
x=3/3
x=1 ans.