How many solutions does this system have?   {y = -1/5x + 6 {3y = 2x - 5   1. 1 solution 2. 2 solutions 3. No solutions 4. Infinite solutions

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The system of equations consists of the equations:

y = (-1/5)*x + 6...(1)

3y = 2x - 5...(2)

Substitute `y = (-1/5)*x + 6` in (2)

=> `3*((-1/5)*x + 6) = 2x - 5`

=> `-3/5*x + 18 = 2x - 5`

=> `(2+3/5)*x = 23`

=> `13/5*x = 23`

=> `x = 115/13`

y = `55/13`

The system of equations has one solution.

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