SOLUTION: solve the system algebraically. Find the number of solutions for the system
{2x-y=-2
{-6x+6y=6
Algebra.Com
Question 627084: solve the system algebraically. Find the number of solutions for the system
{2x-y=-2
{-6x+6y=6
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
solve the system algebraically. Find the number of solutions for the system
{2x-y=-2
{-6x+6y=6
-------
Rearrange and modify:
y = 2x +2
y = x + 1
-----
Substitute for "y" and solve for "x":
2x+2 = x+1
x = -1
----
Solve for "y":
y = 2x +2
y = 2 + 2
y = 4
==============
Cheers,
Stan H.
=============
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Multiply the first equation by 3, then add the two equations term-by-term. Solve the resulting single-variable equation in 
for . Once you have a value for , substitute that value for in either of the original equations and solve the resulting single-variable equation for 
. If at any point the result is a triviality, such as 
, then you have a dependent system (infinite solutions). If at any point the result is an absurdity, such as 
, then you have an inconsistent system (no solution). Otherwise, you have a consistent and independent system with a solution set consisting of a single ordered pair formed from the calculated values of and .
John
My calculator said it, I believe it, that settles it
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