Example

Determining Whether Ordered Pairs are Solutions of {x−3y=−8,;−3x−y=4}\{x - 3y = -8,; -3x - y = 4\}

Determine whether each ordered pair is a solution to the system {x−3y=−8,;−3x−y=4}\{x - 3y = -8,; -3x - y = 4\}

ⓐ Testing (2,−2)(2, -2): Substitute x=2x = 2 and y=−2y = -2 into both equations.

  • First equation: 2−3(−2)=2+6=82 - 3(-2) = 2 + 6 = 8. Since 8≠−88 \neq -8 is false, the first equation is not satisfied.
  • Second equation: −3(2)−(−2)=−6+2=−4-3(2) - (-2) = -6 + 2 = -4. Since −4≠4-4 \neq 4 is false, the second equation is not satisfied.

Because (2,−2)(2, -2) does not make both equations true, it is not a solution of the system.

ⓑ Testing (−2,2)(-2, 2): Substitute x=−2x = -2 and y=2y = 2 into both equations.

  • First equation: −2−3(2)=−2−6=−8-2 - 3(2) = -2 - 6 = -8. Since −8=−8-8 = -8 is true, the first equation is satisfied.
  • Second equation: −3(−2)−2=6−2=4-3(-2) - 2 = 6 - 2 = 4. Since 4=44 = 4 is true, the second equation is satisfied.

Because (−2,2)(-2, 2) makes both equations true, it is a solution of the system.

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Updated 2026-06-18

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