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What is the solution of the system of equations that contains the equation minus 3 x minus 9 y equal 18 and the equation of the line shown on the graph below?

What is the solution of the system of equations that contains the equation minus 3 x minus 9 y equal 18 and the equation of the line shown on the graph below class=

Respuesta :

mhanifa

Answer:

  • Infinite solutions

Step-by-step explanation:

Given equation of the line:

  • - 3x - 9y = 18

Use two points from the graph of the second line to find its equation:

  • (- 6, 0) and (0, - 2)

Use double intercept form to find the equation:

  • x/a + y/b = 1
  • x/ (-6) + y/(- 2) = 1
  • 2x + 6y = - 12

Now we have the system, solve it by elimination.

Multiply the first equation by 2 and the second equation by 3 and add up:

  • 2(- 3x - 9y) + 3(2x + 6y) = 2*18 + 3*(- 12)
  • -6x - 18y + 6x + 18y = 36 - 36
  • 0 = 0

All terms are cancelled, it means the equations are same, the lines overlap and there is infinite number of solutions.

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