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Does this system of equations have one solution, no solutions, or an infinite number of solutions?2x + 3y = 64x + 6y = 12

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Answer:

One solution

Explanation:

There is 3 possible solutions to a system of linear equations:

  • One solution - two distinct lines that do not share y-intercept or slop intersect at a point
  • No solution - two distinct lines that share the same slope but not the same y-intercept never intersect and are parallel
  • Infinite solution - one distinct function represented two ways which in simplest form share the same slope and y-intercept

These equations do not have the same slope or y-intercept. When graphed they intersect at one point.

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