2x+y=4
-3x+ 9y=-6
what is the point on a graph that they share

We'll solve this system of equations by multiplying one of the equations to cancel one of the variables when we add them together.  This will allow us to solve for the other variable.  We then take that variable and plug it into the other equation and solve for the other variable.

Let me show you...

 2x + y = 4    => if we multiply by -9, the y's will cancel
-3x + 9y = -6

(-9)2x + (-9)y = (-9)4
-3x + 9y = -6

-18x -9y = -36
-3x + 9y = -6        Now add the equations together (9y cancels)


-21x = -42
x = -42/-21 = 2  This represents the x value where the lines                              intersect.

Now substitute into the equation

-3x + 9y = -6
-3(2) + 9y = -6
-6 +9y = -6
9y = 0
y = 0/9= 0    This is the y value of the point of intersection

Point of intersection is

(2, 0)