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What is the system of equations shown in the graph? (1 point) Responses {y=2x−3y=3x−4 enlraged left brace start layout first row y equals 2 x minus 3 second row y equals 3 x minus 4 end layout {y=3x+2y=4x+3 enlarged left btrace start layout first row y equals 3 x plus 2 second row y equals 4 x plus 3 end layout {y=2x+3y=3x+4 enlarged left brace start layout first row y equals 2 x plus 3 second row y equals 3 x plus 4 end layout {y=−x+1y=2x+7 enlarged left brace start layout first row y equals negative x plus 1 second row y equals 2 x plus 7 end layout Skip to navigation

image shows two lines overlapping at -1, 1

1 answer

To determine the system of equations represented by the graph with the two lines overlapping at the point (-1, 1), we can substitute the x- and y-values into each equation option to see which pair results in two equations that intersect at that point.

  1. For the first option:
  • \(y = 2x - 3\)

Substituting \(x = -1\): \[ y = 2(-1) - 3 = -2 - 3 = -5 \] which does not equal 1, so this equation does not pass through (-1, 1).

  • \(y = 3x - 4\)

Substituting \(x = -1\): \[ y = 3(-1) - 4 = -3 - 4 = -7 \] which does not equal 1, so this equation does not pass through (-1, 1).

  1. For the second option:
  • \(y = 3x + 2\)

Substituting \(x = -1\): \[ y = 3(-1) + 2 = -3 + 2 = -1 \] which does not equal 1, so this equation does not pass through (-1, 1).

  • \(y = 4x + 3\)

Substituting \(x = -1\): \[ y = 4(-1) + 3 = -4 + 3 = -1 \] which does not equal 1, so this equation does not pass through (-1, 1).

  1. For the third option:
  • \(y = 2x + 3\)

Substituting \(x = -1\): \[ y = 2(-1) + 3 = -2 + 3 = 1 \] which equals 1, so this equation does pass through (-1, 1).

  • \(y = 3x + 4\)

Substituting \(x = -1\): \[ y = 3(-1) + 4 = -3 + 4 = 1 \] which also equals 1, so this equation also passes through (-1, 1).

  1. For the fourth option:
  • \(y = -x + 1\)

Substituting \(x = -1\): \[ y = -(-1) + 1 = 1 + 1 = 2 \] which does not equal 1, so this equation does not pass through (-1, 1).

  • \(y = 2x + 7\)

Substituting \(x = -1\): \[ y = 2(-1) + 7 = -2 + 7 = 5 \] which does not equal 1, so this equation does not pass through (-1, 1).

The correct system of equations that intersects at the point (-1, 1) is:

  • \(y = 2x + 3\)
  • \(y = 3x + 4\)

Therefore, the answer is: {y=2x+3, y=3x+4}.