# Need algebra help with 2 x 2 system or linear equations that are inconsistent or consistent dependent

label Algebra
account_circle Unassigned
schedule 1 Day
account_balance_wallet \$5

Nov 19th, 2015

Question 1

First, we need to add algebraically both equations. We add all what we have on the left side of each equation equal to the addition of all what we have on the right side of each equation. So we would have:

x - 3y = - 3

- x + 3y = - 3

--------------------

x - x - 3y + 3y = - 3 - 3     --------------->   0 + 0 = - 6     ---------------->   0 = - 6 (false identity or equality).

As we can see all the x's and y's cancel out leaving a false equality. So when this happens then it means that the system has no solution.

Final answer: The system has no solution.

Question 2

- x + 5y - 5  =   0

x - 5y      =  - 5

--------------------------

- x + x + 5y - 5y - 5 = 0 - 5    --------------->  0 + 0 - 5 = 0 - 5    ----------------> - 5 = - 5 (true equality or identity).

So again, as we can see all the x's and y's cancel out leaving a true equality (- 5 = - 5). So when this happens then it means that the system has infinitely many solutions. After this, we just need to choose the 1st r 2nd equation and we solve for y like this.

- x + 5y - 5 = 0    ------------> - x + x + 5y - 5 = 0 + x   ------------->  0 + 5y - 5 = x    -------------> 5y - 5 = x

5y - 5 = x  --------------> 5y - 5 + 5 = x + 5    ------------->  5y + 0 = x + 5  -------------> 5y = x + 5

5y = x + 5  ------------->  5y/5 = x/5 + 5/5    --------------> y = 1/5x + 1

Final answer:  The system has infinitely many solutions.

They must satisfy the following equation: y = 1/5x + 1

Nov 19th, 2015

...
Nov 19th, 2015
...
Nov 19th, 2015
Nov 20th, 2017
check_circle