Please explain the steps!?

Question

Solve the system by substitution if possible.

{2x-7y=-13

{3x+14y=-16

Please enter your answer as an ordered pair in the form (x,y).

Answer 1

ok, this should be pretty easy.  the first thing you want to do is to get one of the variables in the first equation by itself.  let's go with x.  so to cancel out the 7y, add 7y to both sides.  

you now have 2x=7y-13.  

now divide both sides by 2.  you get x=(7y-13)/2

now you are going to substitute the value we just found in place of x in the second equation.

3[(7y-13)/2]+14y=-16.

distribute the three:  (21y-39)/6+14y=-16.

now you need to start separating y from the rest of the equation, so multiply 6 to both sides.  21y-39+14y=-96.

add like terms (in this case y's):  35y-39=-96.

add 39 to both sides: 35y=-57

now divide both sides by 35:  y=-57/35.  y=-1.63

now that you know what y is, substitute that back into the first equation.  2x-7(-57/35)=-13.

distribute the 7:  2x+(399/245)=-13

do 399/245.      2x+1.63=-13

subtract 1.63 from both sides:  2x=-14.63

divide both sides by 2:  x=7.32

your answer in (x,y) format:  (7.32, -1.63)

Answer 2

2x-7y=-13 --> 2x = 7y-13 --> x =(7y-13)/2

Substitute (7y-13)/2 for x in the below equation

3x+14y=-16

3(7y-13)/2 +14y = -16

21y/2 -39/2 +14y = -16

21y -39 +28y = -32

49y = 7

y = 1/7

3x +14(1/7) = -16

3x = -18

x = -6

So answer is (-6, 1/7)

Answer 3

2x-7y=-13---------1

3x+14y=-16---------2

equation 1*3 while equation 2*2 so u'll get

{6x-21y=-39---------3

{6x+28y=-32-------4

(equation 3) - (equation 4)

-49y=-7

so y=1/7

put y=1 on your first equation then

x=-6

Answer 4

Srry, saw, substitution, but read elimination...

solve one eq for x or y

2x-7y=-13

2x=7y-13

x = (7y-13)/2 now plug this into the 2nd eq for x

3((7y-13)/2)+14y=-16

((21y - 39)/2) + 14y = -16 mult everything by 2

21y-39 + 28y = -32

49y = 7

y = 7/49 or 1/7 now plug this into second eq

3x + 1/7(14) = -16

3x + 2 = -16

3x = -18

x = -6

(-6, 1/7)

Answer 5

Let 2x-7y=-13----(1) &

3x+14y=-16-----(2)

then,from (1) get

x=(7y-13)/2 which is put in (2),get

3(7y-13)/2+14y=-16=>

49y=7=>

y=1/7------(3)

from (1) & (3),get

2x-7(1/7)=-13=>

x=-6

So, the solution is (-6,1/7)