The following system of equations has to be solved:

x = y - 6 ...(1)

3x + 2y = 2 ...(2)

From (1) x = y - 6

Substitute for x in (2)

=> 3x + 2y = 2

=> 3(y - 6) + 2y = 2

=> 3y - 18 + 2y = 2

=> 5y = 20

=> y = 4

Substitute y = 4 in (1)

=> x = 4 - 6 = -2

**The solution of the set of equations is x = -2 and y = 4**

The system of equations x=y-6 and 3x+2y=2 has to be solved for x. Start with the equation 3x+2y=2 and express x in terms of y.

3x+2y=2

3x = 2 - 2y

x = (2 - 2y)/3

Substitute this in the equation x = y - 6

(2 - 2y)/3 = y - 6

2 - 2y = 3y - 18

5y = 20

y = 20/5 = 4

x = (2 - 8)/3 = -6/3 = -2

The solution of the system of equations is x = -2 and y = 4

x=y-6

=>3x=3y-18

### 3x+2y=2

=>3y-18+2y=2

=>5y-18=2

=>5y=2+18

=>5y=20

=>y=20/5

=>y=4

### x=y-6

=>x=4-6

=>x=-2

The given equations are:

x = y - 6 ... (1)

3x + 2y = 2 ... (2)

Substituting (1) in (2), we get

3(y-6) + 2y = 2

=> 3y - 18 + 2y = 2

=> 5y - 18 = 2

=> 5y = 2 + 18

=> 5y = 20

=> y = 4 ... (3)

Substituting y = 4 in(1), we get

x = 4 - 6, that is x = -2 ... (4)

From (3) and (4), ** X = -2 AND Y = 4**.