Question

3x+y =7
3x+y=10 if the system cannot be solved state that it cannot be solved and explain why... plzz help!!

Answer 1

3x+y=7
3x+y=10

subtract one equation from the other, what do you get?

Answer 2

3x+y=17?

Answer 3

not quite
subtracting one equation from the other looks like this:
3x+y=7
-(3x+y=10)
-----------
(3x+y)-(3x+y)=7-10

simplify^^^^
what do you get?

Answer 4

y=-3?

Answer 5

closer, but the left hand side is still wrong:
(3x+y)-(3x+y)=0
so it should be...?

Answer 6

-3?

Answer 7

you need to write the whole equation
-3 is on the right, what's on the left side?

Answer 8

im guessing nothing right?

Answer 9

not nothing
as I said
(3x+y)-(3x+y)=0
and 0 is different than nothing (though it may not seem that way)

Answer 10

ok so its 0=-3?

Answer 11

yes :)
and is that ever a true statement?

Answer 12

no so this system doesnt have a solution?

Answer 13

correct :)
nice job!

Answer 14

thank you!!

Answer 15

welcome!
there are faster ways to see that this has no solution
perhaps jim_thompson will explain another method

Answer 16

Another way to look at this:


If we let z = 3x+y, then


we go from


3x+y = 7
3x+y = 10


to


z = 7
z = 10


Since z is a single number, it is impossible for it to be equal to BOTH 7 and 10 at the same time. So there are no solutions for z


Consequently, this extends to the fact that there are no solutions for x and y.

Answer 17

thank you!

Answer 18

yes, that's the slick way to look at it :)

Answer 19

lol!

Answer 20

Another way is to use substitution

Solve 3x+y = 7 for y to get y = -3x+7. Now plug this into the second equation


3x+y = 10

3x+(-3x+7) = 10

3x-3x + 7 = 10

0x + 7 = 10

7 = 10 ....which is NEVER true...so there are NO solutions


Whatever method you use, you'll find that there are no solutions.