Solve the system of equations 3x-y=9 & 2x+y=1?

3x - y = 9
2x + y = 1

5x = 10
x = 2

3x - y = 9
3(2) - y = 9
6 - y = 9
-y = 3
y = -3

(2, -3)

Value of x:
3x - 9 = 1 - 2x
5x = 10
x = 2

Value of y (1st equation):
3(2) - y = 9
6 - y = 9
y = - 3

Answer: x = 5, y = - 3

Proof (2nd equation):
2(2) - 3 = 1
4 - 3 = 1
1 = 1

5x = 10
x = 2

4 + y = 1
y = - 3

x = 2 , y = - 3

3x - y = 9 (solve by using elimination)
2x + y = 1

...3x - y = 9
+) 2x + y = 1 (addition)
------------------------
5x = 10

5x = 10
x = 10/5
x = 2

3x - y = 9
3(2) - y = 9
6 - y = 9
y = 6 - 9
y = -3

∴ x = 2 , y = -3

using elimination:
Given:
3x-y=9 (equation 1)
2x+y=1 (equation 2) (y-y=0) the equation will be::
--------------
5x=10 (divide all terms by 5 to get the value of x)
x=2

substitute x=2 to equation 1(or any of the equation)

3x-y=9
3(2)-y=9
-y=9-6
-y=3 (divide all terms by -1)
y = -3

Therefore x=2 and y=-3

x=(1-y)/2
3(1-y)/2-y=9
3/2-3y/2-y=9
5y/2=3/2-9

y=3/5-18/5=-15/5 =-3

2x-3=1
x=2

3x-y =9
(+)
2x+y=1
--------------
5x =10
x =2

substitute x=2 to any of the equation:
3(2)-y=9
6 -y=9
-y=9-6
-y=3
y=-3

in conclusion: x=2; y=-3

3x-y=9
2x+y=1

adding the two equations
3x-y=9
2x+y=1
-----------------
5x=10
x=10/5 = 2

replace x in first equation
3(2)+y=9
6+y=9
y=9-6
y=3

x=2, y=3

x=2
y=-3

about a million ways to do this one. Add the equations together so you get 3x-y+2x+y=9+1, the y's cancel, so you have 5x=10, so x=2. Plug X=2 into the first equation, you get 3*2-y=9, therefore -y=9-6=3, so y=-3

3x - y = 9
2x + y = 1

<=>

5x = 10 <=> x = 2 and y = -3