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Solve the system 2x + y = 7 and x - y = 2

Worked through step by step. More systems.

Answer
x=3,y=1\boxed{x = 3, y = 1}

Checking the result by substituting into the first equation: 2(3)+(1)=6+1=72(3) + (1) = 6 + 1 = 7, which is correct.

Problem: Solve the system of linear equations {2x+y=7x−y=2\begin{cases} 2x + y = 7 \\ x - y = 2 \end{cases}.

Steps

  1. Add both equations to eliminate yy
    (2x+y)+(x−y)=7+2(2x + y) + (x - y) = 7 + 2
  2. Simplify the equation
    3x=93x = 9
  3. Divide both sides by 3
    x=3x = 3
  4. Substitute x=3x = 3 into the second equation
    3−y=23 - y = 2
  5. Subtract 3 from both sides
    −y=−1-y = -1
  6. Multiply both sides by -1
    y=1y = 1

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