SOLUTION: x-y=5 3x+2y=-1

Click here to see ALL problems on Linear-systems

Question 1028483: x-y=5
3x+2y=-1

Found 2 solutions by stanbon, addingup:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
x-y=5
3x+2y=-1
-----
Modify for elimination:
2x - 2y = 10
3x + 2y = -1
-------------------
Add and solve for "x"::
5x = 9
x = 9/5
--------
Solve for "y"::
y = x-5
y = 9/5 - 5
y = (9-25)/5 = -16/5 = - 3 1/5
------------------------
Cheers,
Stan H.
---------------

Answer by addingup(3677) (Show Source):
You can put this solution on YOUR website!
x-y=5 Multiply both sides times 2 and add to the one below
3x+2y=-1
~~~~~~~~~~~~~~~~~~~~~~~~~~~
2x-2y=10
+
3x+2y=-1
---------
5x = 9
x = 9/5 = 1 1/4
Now you can solve for y. Take any one of the two equations, I'll use the first one:
x-y = 5
9/5-y = 5 multiply both sides times 5
9-5y = 25 Subtract 9 on both sides
-5y = 16
Divide both sides by -5
y = -16/5 = -3 1/5
~~~~~~~~~~~~~~~~~~~~
Check: To check my answers, I use the second equation:
3x+2y=-1 Substitute with the values I got for x and y:
3(9/5)+2(-16/5)= -1 Multiply both sides times 5
3(9)+2(-16) = -5
27-32 = -5 Correct
NOTE: you can also do this, since multiplying fractions is so easy:
3(9/5)+2(-16/5)= -1 Multiply 3/1*9/5=(3*9)/(1*5) and 2/1*-16/5=(2*-16)/(1*5)
27/5-32/5 = -1
-5/5 = -1 Correct