anonymous
  • anonymous
The system, 6x - 4y = 5 and 9x - 6y = 5, is consistent. True False
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
6x - 4y = 5 --> (3)6x - 4y = 5 9x - 6y = 5 -->(-2)9x - 6y = 5 ---------- 12x - 12y = 15 (result of multiplying by 3) -18x + 12y = -10 (result of multiplying by -2) ----------add -6x = 5 x = - 5/6 now sub - 5/6 in for x into either of the original equations 9x - 6y = 5 9(-5/6) - 6y = 5 -45/6 - 6y = 5 -45/6 - 5 = 6y -45/6 - 30/6 = 6y -75/6 = 6y (-75/6)/6 = y -75/6 x 1/6 = y - 75/36 = y - 25/13 = y check.. 6x - 4y = 5 6(-5/6) - 4(-25/13) = 5 -5 + 100/13 = 5 - 65/13 + 100/13 = 5 35/13 = 5 2 9/13 = 5 (incorrect) False. The system of equations is not consistent. An equation is consistent if it has a solution. If it does not have a solution, it is not consistent.

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