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Solve by substitution y = x + 3 and 2x + y = 12

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Answer
x=3,y=6 or (3,6)\boxed{x = 3, y = 6 \text{ or } (3, 6)}

Substituting x=3x = 3 and y=6y = 6 into the original equations gives 6=3+36 = 3 + 3 and 2(3)+6=122(3) + 6 = 12, both of which are true.

Problem: Solve the system of equations by substitution: y=x+3y = x + 3 and 2x+y=122x + y = 12.

Steps

  1. Substitute yy in the second equation
    2x+(x+3)=122x + (x + 3) = 12
  2. Combine like terms
    3x+3=123x + 3 = 12
  3. Subtract 3 from both sides
    3x=93x = 9
  4. Divide both sides by 3
    x=3x = 3
  5. Substitute xx back into the first equation to find yy
    y=3+3y = 3 + 3
  6. Simplify for yy
    y=6y = 6

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