Question

how many solutions are there to the following system of equations?
4x-14y=6
-2x+7y=-3
a. 0
b. 1
c. 2
d. infinitely number of solutions

Answer 1

@Qwertty123

Answer 2

@Flower-girl

Answer 3

if you multiply the second equation by 2 (that means both sides and all terms) you get
-4x+14y= - 6
now add that to the first equation, term by term:
4x - 14y = 6
-4x +14y = - 6
you get
0 + 0 = 0
or
0=0
which is true. This means the system of equations is true no matter what x and y are
since x can be any number (and once we know x we can find a y that goes with it)
we have lots of solutions

Answer 4

another way to figure it out:

4x-14y=6
-2x+7y=-3
if you multiply the second equation by -2 you get
4x - 14y = 6
which is identical to the first equation

for every (x,y) pair that works for the first equation, it will also work for the 2nd
in other words, lots of solutions work for both equations (being the same line)

Answer 5

ok! can you help me with another one?