Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 months ago

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

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  • 4 months ago
    Favorite 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 s
    Lv 7
    4 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

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