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# Find u and v if u+4v=4i-k and 4u-v=i+j+k.?

Find u and v if u+4v=4i-k and 4u-v=i+j+k.

I tried to set them equal to each other but now I am lost. Thanks in advance.

### 2 Answers

- llafferLv 74 months agoFavorite Answer
If you treat i, j, and k as constants, you have two variables and two unknowns that you can solve in terms of the three constants:

u + 4v = 4i - k and 4u - v = i + j + k

Let's solve the first equation for u in terms of v:

u + 4v = 4i - k

u = 4i - k - 4v

Now substitute that into the other equation and solve for v:

4u - v = i + j + k

4(4i - k - 4v) - v = i + j + k

16i - 4k - 16v - v = i + j + k

-17v = -15i + j + 5k

v = (15i - j - 5k) / 17

Now substitute that back in the original equation and solve for u:

u + 4v = 4i - k

u + 4(15i - j - 5k) / 17 = 4i - k

Let's start with multiplying both sides by 17 to get rid of the fraction for now:

17u + 4(15i - j - 5k) = 68i - 17k

17u + 60i - 4j - 20k = 68i - 17k

17u = 8i + 4j + 3k

u = (8i + 4j + 3k) / 17

So your solution is:

u = (8i + 4j + 3k) / 17 and v = (15i - j - 5k) / 17

- ted sLv 74 months ago
you have system : to solve multiply the 2nd by ' 4 ' and add to the 1st : 17 u = 8 i + 4 j + 3 k...find u , then v