Solve the simultaneous equation p=3q 4p₅q =14 a₆2 c₆

Mathematics

ScanSolve AI Answer

Answer

p=6p = 6

q=2q = 2

Step-by-step solution

3 steps

To solve the simultaneous equations p=3qp = 3q and 4p−5q=144p - 5q = 14:

  1. Substitute the first equation into the second equation.

    Given the first equation p=3qp = 3q.
    Substitute this expression for pp into the second equation 4p−5q=144p - 5q = 14:

    4(3q)−5q=144(3q) - 5q = 14
  2. Simplify and solve for qq.

    12q−5q=1412q - 5q = 14 7q=147q = 14 q=147q = \frac{14}{7} q=2q = 2
  3. Substitute the value of qq back into the first equation to find pp.

    Using p=3qp = 3q:

    p=3(2)p = 3(2) p=6p = 6

    The solution to the simultaneous equations is:
    p=6p = \boxed{6}
    q=2q = \boxed{2}

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