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

Question

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

jim_thompson5910 · Answer

Multiply every term in the 2nd equation by 4 to get  -4x+12y=24

So we now have


  4x+2y=8
-4x+12y=24

jim_thompson5910 · Answer

Add the equations and tell me what you get

anonymous · Answer

y=42?

jim_thompson5910 · Answer

no

jim_thompson5910 · Answer

Add the equations to get


  4x+2y=8 
-4x+12y=24
-------------
0x + 14y = 32


So 14y = 32


Solve that for y

anonymous · Answer

y=16/7

jim_thompson5910 · Answer

good

jim_thompson5910 · Answer

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

jim_thompson5910 · Answer

So the answer is   d. one solution

anonymous · Answer

thank you!

jim_thompson5910 · Answer

Notice how they're not asking what the solutions are, they just want to know how many there are

jim_thompson5910 · Answer

you're welcome

anonymous · Answer

so with other problems like that, how would I know how many solutions there are?

jim_thompson5910 · Answer

follow the same method and see if you get a solution for either variable. If you do, then it has one solution