What point on the graph do these two equations go through?

y = -2x + 2  (1)

3x + 2y = 1  (2)

Substitution ......put (1)  into (2)

3x + 2 [ -2x + 2]  = 1

3x - 4x + 4  = 1

-x  = -3

x = 3      and    y = -2(3) + 2   = -4

Subtraction :

y = -2x + 2    →   2x + y = 2   (1)

3x + 2y = 1    (2)

Multiply (1) by 2

 4x +2y  = 4

 3x + 2y  = 1       subtract the second from the first

x  = 3         and   y  = -2(3) + 2  = -4

Graph :  https://www.desmos.com/calculator/xxjyr6ljsh

You have the value for y =  -2x + 2   Substitute this 'y' into equation 2

3x +2 (-2x+2) = 1    and solve for 'x'

3x -4x + 4 = 1

-x = -3     x = 3        Now y=-2x + 2     substitute x = 3   y = -2(3) + 2 = -6 +2 = -4

x,y    =  3,-4

Multiply both sides of first eq by  2 to get      2y =- 4x+4    or re-written as 4x + 2y = 4   and subtract this from the second equation

          3x + 2y = 1

   -      4x + 2y =4

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          -x  = -3        x = 3      Substitute to find y = -4

Graph using the calculator to see where the lines intersect.....sorry can't show you this....

~jc