could someone help me with this please?

Question

4y+8x=6

-2y-4x=-3

 

my mindset for it was..changing the equation around to 8x=-4y+6 over -4x=2y-3

 

and then i thought to plug them in 8(2y-3)+4y=6

and got 16y-24+4y=6

and it didn't come out correctly. what do i do? its so frustating

Answer 1

4y+8x=6  ...first equation
-2y-4x=-3....second equation

 

my mindset for it was..changing the equation around to            8x=-4y+6  ⇐CORRECT!

THEN YOU DIVIDED EACH TERM BY NEGATIVE TWO:     over     -4x=2y-3    ⇐CORRECT!

 

Then in the second (original) equation, replacing -4x by 2y - 3, you get:

 

-2y + 2y - 3 = -3; continuing, you get -3 = -3, so the second equation has, in effect, disappeared!

 

THIS IS CORRECT; therefore there are NOT two different equations here. The solution is the ONE LINE having equation 2y + 4x = 3.  There are INFINITELY MANY points in the solution set.

 

So you now have experienced the disappearing equation, of it's not a system, it's just one line, situation.

 

Go back to the first two equations; you can see that, if you had divided the first equation by -2, you'd get the second equation; this is called a DEPENDENT situation.

 

Study & Learn!!  Best wishes.  KS

Answer 2

 

(i)    4y+8x=6
(ii)   -2y-4x=-3

 

Note that if you divide equation (i) by -2, you get equation (ii):

 

(1/-2)(4y+8x) = (1/-2)6

-2y-4x = -3

 

So equation (ii) is really just a multiple of equation (i).  You do not have two independent equations, and therefore you cannot solve for the two unknowns x and y.  This problem does not have a unique solution.