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Solve the simultaneous equations: 3m + n = -5, m = 1 − 3n

Mathematics

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Answer

m=−2,n=1m = -2, n = 1

Step-by-step solution

5 steps

Here are the simultaneous equations:

  1. 3m+n=−53m + n = -5
  2. m=1−3nm = 1 - 3n

  1. Substitute the expression for mm from equation (2) into equation (1).

    3(1−3n)+n=−53(1 - 3n) + n = -5

  2. Distribute the 3 and simplify the equation.

    3−9n+n=−53 - 9n + n = -5 3−8n=−53 - 8n = -5

  3. Subtract 3 from both sides of the equation.

    −8n=−5−3-8n = -5 - 3 −8n=−8-8n = -8

  4. Divide by -8 to solve for nn.

    n=−8−8n = \frac{-8}{-8} n=1n = 1

  5. Substitute the value of n=1n=1 back into equation (2) to find mm.

    m=1−3(1)m = 1 - 3(1) m=1−3m = 1 - 3 m=−2m = -2

    The solution to the simultaneous equations is:

    m=−2,n=1m = -2, n = 1
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