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Solve the system 4x - 3y = 11 and 2x + y = 3

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Answer
x=2, y=−1 (or (2,−1))\boxed{x = 2, \ y = -1 \text{ (or } (2, -1))}

Substituting x=2x = 2 and y=−1y = -1 into both original equations makes them true statements (4(2)−3(−1)=114(2) - 3(-1) = 11 and 2(2)+(−1)=32(2) + (-1) = 3).

Problem: Solve the system of linear equations {4x−3y=112x+y=3\begin{cases} 4x - 3y = 11 \\ 2x + y = 3 \end{cases}.

Steps

  1. Solve the second equation for yy
    y=3−2xy = 3 - 2x
  2. Substitute yy into the first equation
    4x−3(3−2x)=114x - 3(3 - 2x) = 11
  3. Distribute
    4x−9+6x=114x - 9 + 6x = 11
  4. Combine like terms
    10x−9=1110x - 9 = 11
  5. Add 9 to both sides
    10x=2010x = 20
  6. Divide by 10
    x=2x = 2
  7. Substitute x=2x = 2 back into the expression for yy
    y=3−2(2)y = 3 - 2(2)
  8. Simplify
    y=−1y = -1

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