Example

Determining Whether Ordered Pairs are Solutions of {3x+y=0,  x+2y=5}\{3x + y = 0,\; x + 2y = -5\}

Determine whether each ordered pair is a solution to the system {3x+y=0,  x+2y=5}\{3x + y = 0,\; x + 2y = -5\}

ⓐ Testing (1,3)(1, -3): Substitute x=1x = 1 and y=3y = -3 into both equations.

  • First equation: 3(1)+(3)=33=03(1) + (-3) = 3 - 3 = 0. Since 0=00 = 0 is true, the first equation is satisfied.
  • Second equation: 1+2(3)=16=51 + 2(-3) = 1 - 6 = -5. Since 5=5-5 = -5 is true, the second equation is satisfied.

Because (1,3)(1, -3) makes both equations true, it is a solution of the system.

ⓑ Testing (0,0)(0, 0): Substitute x=0x = 0 and y=0y = 0 into both equations.

  • First equation: 3(0)+0=03(0) + 0 = 0. Since 0=00 = 0 is true, the first equation is satisfied.
  • Second equation: 0+2(0)=00 + 2(0) = 0. Since 050 \neq -5 is false, the second equation is not satisfied.

Because (0,0)(0, 0) does not make both equations true, it is not a solution of the system.

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Updated 2026-04-24

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