HELP AND PLEASE WORK OUT SO I UNDERSTAND HOW TO DO IT.
2x+7y=1
x+5y=2

Question

HELP AND PLEASE WORK OUT SO I UNDERSTAND HOW TO DO IT.
2x+7y=1
x+5y=2

amistre64 · Answer

any initial thoughts on how to approach it?

amistre64 · Answer

if we take the 2nd equation, we can multiply it by 2 to see what 2x is equivalent to

amistre64 · Answer

2(x+5y=2)

2x+10y =  4
    - 10y   -10y
-------------
      2x = 4 - 10y

everywhere we see a 2x, we can replace it by  4-10y

then see if there is a way to find a solution for y

anonymous · Answer

2x=4-10y?
what next what does x = ?

amistre64 · Answer

forget about x for the moment, and replace all the 2x parts you see with 4-10y

that should give you an idea on what to do next

anonymous · Answer

OK. 2x=4-10y
is the problem finished?

amistre64 · Answer

of course not, there is more to do which is why i suggested that you actually do more.

2x + 7y = 1
^^
replace it

4 - 10y + 7y = 1

amistre64 · Answer

do you agree that this is solvable for y now?

anonymous · Answer

$$x +5y=2$$
$$x=2-5y$$ then substitute the x to 2x+7y=1
$$2(2-5y)+7y=1$$
$$4-10y+7y=1$$
$$4-3y=1$$

anonymous · Answer

$$3y=4-1$$
$$3y=3$$
$$y=1$$ now you have the value of y

anonymous · Answer

so you can substitute it to x+5y=2 to find the x

anonymous · Answer

ok this is what i have on my paper.
2x+7y=1
(x+5y=2)2
now I'm really confused.

amistre64 · Answer

multiply the 2 thru the paranthesis ... distribute it

2x+7y=1
(x+5y=2)2


2x+7y=1
2x+10y=4


now there are a few ways to approach this, substitution or elimination ... both work out fine

anonymous · Answer

well i don't know what to do after distributive

amistre64 · Answer

well, my thought was to solve for 2x, and run a substitution, which i worked thru already.

tblue even worked thru a similar substitution process and determined a specific y value for you.

amistre64 · Answer

the key strategy is simply getting rid of 2 variables so that you only have 1 variable to solve .... and a 1 variable solution is gone over extensively prior to these systems.

4 - 10y + 7y = 1

we can use that to solve for a specific value of y

amistre64 · Answer

if we use the elimination method, we are primed for getting rid of the x parts by subtracting one equation from the other

   2x+7y=1
-(2x+10y=4)


  2x +7y  =  1 
-2x -10y = -4
--------------
  0  -3y  = -3

-3y = -3  when y = ?

amistre64 · Answer

good luck with this, i have to be going