As, we can see the graph, the two lines intersect at exactly one point. Hence, there is just one solution.
Theortically, As the slope of [tex] y=-2(3)x [/tex] and [tex] y=9x-2 [/tex] is different. Hence, the system of equation has exactly one unique solution.
2. The x coordinate of the solution from graph is 0.1333.
Theortically, From, y=-2(3x) and y=9x-2
-2(3x)=9x-2
-6x=9x-2
Adding 2 on both sides, we get,
-6x+2=9x-2+2
-6x+2=9x
Adding 6x on both sides, we get,
2=15x
Dividing by 15 on both sides
x=[tex] \frac{2}{15} [/tex]
x=0.1333
As, x=0.1333 in y=-2(3)x
y=-2(3)([tex] \frac{2}{15} [/tex])
y=[tex] \frac{-2*3*2}{15} =\frac{-2*2}{5} =\frac{-4}{5} [/tex]
y=-0.8
Graphically, as well y coordinate of point of intersection is -0.8
