Given:
y=4x
y=-5x+9
We see that the coefficients of x (i.e. the slopes) are different. Therefore the two lines are not parallel (always has one solution), and are not coincident (does not have infinite solutions).
The next step is to find the intersection point, or solution to the system.
The form of the system is best solved by "comparison", since both equations are equated to y, so we can write directly
However, we are asked to solve by graphing, so we will need to graph the two lines.
As explained previously, the line y=mx+b has a slope of m and y-intercept of b.
For y=4x, it is a line passing through the origin (b=0) with a slope of 4.
For y=-5x+9, it is a line with a slope of -5, passing through (0,9), which is the y-intercept.
Where the two lines meet is the solution expected, as we can read on the graph, (1,4) is the solution to the above system.
Check: y=4x=4(1)=4..... good
y=-5x+9=-5(1)+9=-5+9=4 ..... good
