Question

Solve the following system of equations. Express your answer as an ordered

pair in the format (a,b), with no spaces between the numbers or symbols.
2x+7v= -7
- 4x - 30= - 19

Answer 1

I have two problems and I put both of the answers in (x,v) form.

(-11/4,-3/14) for 2x+7v=-7 and -4x-30=-19

OR

(-343/32 , 33/16) for 2x+7v=-7 and -4x-30v=-19

Explanation:

I will solve the system as is ... but I'm not sure if you want your answer as (x,v) or (v,x)...

Let's go!

The second equation contains only one variable so I'm going to solve it first!

I'm going to solve -4x-30=-19 for x.

-4x-30=-19

Add 30 on both sides

-4x =11

Divide both sides by -4

x =11/-4 or -11/4

So the 1st equation 2x+7v=-7 we are going to use our x=-11/4 to solve for v.

2(-11/4)+7v=-7

-22/4 +7v=-7

-11/2 +7v=-7

7v=-7+11/2

7v=-3/2

v=-3/14

So (x,v) is (-11/4,-3/14).

Now I will also pretend you meant:

2x+7v=-7

-4x-30v=-19

I will do this by elimination.

Multiply the first equation by 2 and your x's will be opposites... And everyone knows when you add opposites you get 0 :).

4x+14v=-14 (I had multiply 2x+7v=-7 by 2 on both sides)

-4x-30v=-19

---------------------- I will now add the equations:

0-16v=-33

-16v=-33

v=33/16

Now to find x... Use one of the equation, doesn't matter which.... Replace v with 33/16 and solve for x.

So I'm going to use 2x+7v=-7 with v=33/16

2x+7(33/16)=-7

2x+231/16=-7

2x =-7-231/16

2x =-343/16

x =-343/32

So the solution in the form (x,v) is (-343/32 , 33/16)

Answer 2

Case 1

The solution is:
`(-(343)/(32), (33)/(16))`

Case 2

The solution is:
`(-(11)/(4),-(3)/(14))`

Explanation:

Case 1

Assuming you want to write the following

`2x+7v= -7`

`-4x -30v= - 19`

----------------------------

Multiply the first equation by 2 and add it to the second equation

`4x+14v= -14`

+

`-4x -30v= - 19`

------------------------------------

`-16v=-33`

`v=(33)/(16)`

Then

`2x+7((33)/(16))= -7`

`2x+(231)/(16)= -7`

`2x= -7-(231)/(16)`

`2x=-(343)/(16)`

`x=-(343)/(32)`

The solution is:
`(-(343)/(32), (33)/(16))`

Case 2

Assuming you want to write the following

`2x+7v= -7`

`-4x -30= -19`

Then solve the second equation for the variable x and then replace the value of x in the first equation

`-4x -30= -19`

`-4x= -19+30`

`-4x= 11`

`x= -(11)/(4)`

Then wehave that:

`2(-(11)/(4))+7v= -7`

`-(11)/(2)+7v= -7`

`7v= -7+(11)/(2)`

`7v= -(3)/(2)`

`v= -(3)/(14)`

The solution is:
`(-(11)/(4),-(3)/(14))`