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Solve the system x + y = 10 and x - y = 4

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Answer
x=7,y=3\boxed{x = 7, y = 3}

Checking the result, 7+3=107 + 3 = 10 and 7−3=47 - 3 = 4, which satisfies both original equations.

Problem: Solve the system of linear equations {x+y=10x−y=4\begin{cases} x + y = 10 \\ x - y = 4 \end{cases}

Steps

  1. Add the two equations
    (x+y)+(x−y)=10+4(x + y) + (x - y) = 10 + 4
  2. Combine like terms
    2x=142x = 14
  3. Divide both sides by 2
    x=7x = 7
  4. Substitute x=7x = 7 into the first equation
    7+y=107 + y = 10
  5. Subtract 7 from both sides
    y=3y = 3

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