Calculate points of intersection of the following two pairs of equations.

We need the point(s) where   y = 5x+6    equals  y = 9x-32    

     or    5x+6 = 9x-32       solve for x     add 32 to each side of the equation

            5x+38 = 9x           subtract 5x from both sides

                  38 = 4 x

                    9.5 = x           Now substitute theis 'x' into one of the equations to find 'y'

          y= 5(9.5) +6        y= 53.5      so   x,y  =  9.5 , 53.5   

  (you can sub 'x' in to the other equation to see if you get the same result as a check)

0.5x+1.5= -4(x-3)

                = -4x +12       add 4x to both sides

4.5x +1.5 =12                 Subtract 1.5 from both sides

4.5x = 10.5                      Divide by 4.5

x = 2 1/3

then sub  this 'x' in to one of the other equations to find 'y'

y=-4(x-3)=-4x+12

 = -4 (2 1/3) + 12 = 2 2/3       x,y = 2 1/3 , 2 2/3