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Mathematics 32 Online
OpenStudy (anonymous):

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

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

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!

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

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