Find the coordinates of the point of intersection of the lines 2x + 3y = 12 and y = 7 - 3x.

We can substitute the equation for y into 2x + 3y = 12.
If y = 7-3x , 2x + 3(7-3x) = 12 2x + 21-9x = 12
Now we can solve for x -7x = =-9x = 9/7
To get y, we must sub x back into y = 7 - 3x, to get the y co-ordinate.
y = 7-3(9/7) y = 7 - 27/7 y = 49/7 - 27/7 y = 22/7
(9/7, 22/7) is our intersection.