Use the substitution method to solve the linear system..u-v = 0 AND 7u+v = 0?

Question

the question is set up like this (also shown above):

u-v=0
7u+v=0

Answer 1

*Solve for "u" or "v" in either equation. Let's solve for "u" in the 1st equation.

First: add "v" to both sides...

u - v + v = 0 + v
u = 0 + v
u = v

Sec: replace "v" with the "u-variable" in the 2nd equation...

7v + v = 0
8v = 0

*Isolate "v" on one side --- divide both sides by "8"...

8v/8 = 0/8
v = 0

Third: replace "0" with the "v-variable" in the 1st equation...

u - 0 = 0
u = 0

Solution: (0, 0)

Answer 2

In the substitution method, you isolate one of the variables.

Let's take the first equation: u = 0 + v
...now substitute 0 + v for u in the second equation:

7(0 + v) = 0

Simplify: 7v = 0
... and solve for v: v = 0/7 = 0

... now put that value (0) back into the equation (either one) to find u: u = 0 + 0 = 0.

... so u = 0 and v = 0

Answer 3

u-v=0
7u+v=0

You can use the first equation and add v to both sides. You get u=v. Now, you can plug in u in the second equation and you get 7v+v=0.

Combine to get 8v=0
Divide by eight to get v=0

Now that you know that v=0, you can plug it back into the equation u=v and you get that v=0, and u=0

Answer 4

Add these two together to get 8u=0 from which you know that u=0. But this requires v to also equal zero.

Answer 5

isolate u
u=v
substitue u into equation 2
7v+v=0
combine like terms
8v=0
v=0
substitue v back into equation 1
u=0