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which ordered pair is the solution to the system of linear equations \\…

Question

which ordered pair is the solution to the system of linear equations \\(y = 5x + 8\\) and \\(y = -4x - 1\\)?

  • \\((1, -3)\\)
  • \\((3, -1)\\)
  • \\((-1, 3)\\)
  • \\((-3, 1)\\)

Explanation:

Set the equations equal to each other

Using the Substitution Method and System of Equations knowledge points

$$ LATEXBLOCK0 $$

Solve for x

Using the Substitution Method knowledge point

$$ LATEXBLOCK1 $$

Solve for y

Using the Substitution Method knowledge point

$$ LATEXBLOCK2 $$

Verify the solution

Using the Substitution Method knowledge point

$$ LATEXBLOCK3 $$

Answer:

  • (A) \((1,-3)\)
  • (B) \((3,-1)\)
  • (C) \((-1,3)\) (Correct answer)
  • (D) \((-3,1)\)