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

### 1 Answer | Add Yours

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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