Solve the system of equations by any methods. 2x-3y+1=0 x+y-2=0

The system can be solved either using elimination method,
or substitution method.

We'll choose elimination method to
remove y variable. For this reason we'll multiply the 2nd equation by
3:

3x + 3y - 6 = 0

We'll add
this equation to the 1st equation of the system:

3x + 3y -
6 + 2x - 3y + 1 = 0

We'll eliminate variable
y:

5x - 5 = 0

We'll isolate 5x
to the left side, adding 5 both sides:

5x =
5

x = 1

We'll replace x by 1
within the second equation, to determine y:

1 + y - 2 =
0

y = 2 - 1

y =
1

The solution of the system of independent
equations is (1 ; 1).