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Solve the system of equations. (calculator/graph recommended) \( y = -\frac{1}{2}x + 3 \) \( -x + y = -3 \)...

Solve the system of equations. (calculator/graph recommended)
\( y = -\frac{1}{2}x + 3 \)
\( -x + y = -3 \)
(-1, -4)
(-4, 7)
(1, 4)
(4, 1)

Answer

To solve the system of equations:

  1. Substitute \( y = -\frac{1}{2}x + 3 \) into \( -x + y = -3 \).
  2. \( -x + (-\frac{1}{2}x + 3) = -3 \)
  3. \( -x - \frac{1}{2}x + 3 = -3 \)
  4. \( -\frac{3}{2}x + 3 = -3 \)
  5. \( -\frac{3}{2}x = -6 \)
  6. \( x = 4 \)
  7. Substitute \( x = 4 \) back into \( y = -\frac{1}{2}x + 3 \).
  8. \( y = -\frac{1}{2}(4) + 3 \)
  9. \( y = -2 + 3 \)
  10. \( y = 1 \)
  11. The solution is \((4, 1)\).

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