Example

Determining Whether Ordered Pairs are Solutions of {x3y=8,  3xy=4}\{x - 3y = -8,\; -3x - y = 4\}

Determine whether each ordered pair is a solution to the system {x3y=8,  3xy=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: 23(2)=2+6=82 - 3(-2) = 2 + 6 = 8. Since 888 \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 44-4 \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: 23(2)=26=8-2 - 3(2) = -2 - 6 = -8. Since 8=8-8 = -8 is true, the first equation is satisfied.
  • Second equation: 3(2)2=62=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.

0

1

Updated 2026-04-24

Contributors are:

Who are from:

Tags

OpenStax

Intermediate Algebra @ OpenStax

Ch.4 Systems of Linear Equations - Intermediate Algebra @ OpenStax

Algebra

Related