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

Answer 1

Multiply every term in the 2nd equation by 4 to get -4x+12y=24

So we now have


4x+2y=8
-4x+12y=24

Answer 2

Add the equations and tell me what you get

Answer 3

y=42?

Answer 4

no

Answer 5

Add the equations to get


4x+2y=8
-4x+12y=24
-------------
0x + 14y = 32


So 14y = 32


Solve that for y

Answer 6

y=16/7

Answer 7

good

Answer 8

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

Answer 9

So the answer is d. one solution

Answer 10

thank you!

Answer 11

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

Answer 12

you're welcome

Answer 13

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

Answer 14

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