How many solutions does the system of equations have?
4x+2y=8
-x+3y=6
a. two solutions
b. infinitely many
c. no solution
d. one solution
Still Need Help?
Join the QuestionCove community and study together with friends!
Sign Up
jimthompson5910 (jim_thompson5910):
Multiply every term in the 2nd equation by 4 to get -4x+12y=24
So we now have
4x+2y=8
-4x+12y=24
jimthompson5910 (jim_thompson5910):
Add the equations and tell me what you get
OpenStudy (anonymous):
y=42?
jimthompson5910 (jim_thompson5910):
no
jimthompson5910 (jim_thompson5910):
Add the equations to get
4x+2y=8
-4x+12y=24
-------------
0x + 14y = 32
So 14y = 32
Solve that for y
Still Need Help?
Join the QuestionCove community and study together with friends!
Sign Up
OpenStudy (anonymous):
y=16/7
jimthompson5910 (jim_thompson5910):
good
jimthompson5910 (jim_thompson5910):
Then use this to find x
You don't need to find x. The mere fact that you found a solution for y (and that you CAN find a solution for x) suggests that a unique solution exists
jimthompson5910 (jim_thompson5910):
So the answer is d. one solution
OpenStudy (anonymous):
thank you!
Still Need Help?
Join the QuestionCove community and study together with friends!
Sign Up
jimthompson5910 (jim_thompson5910):
Notice how they're not asking what the solutions are, they just want to know how many there are
jimthompson5910 (jim_thompson5910):
you're welcome
OpenStudy (anonymous):
so with other problems like that, how would I know how many solutions there are?
jimthompson5910 (jim_thompson5910):
follow the same method and see if you get a solution for either variable. If you do, then it has one solution