SOLUTION: This question has been confusing me and I really need some help. Thank You! Find the solution of the system of equations by graphing. y=-x+9 y=4x-1 Thank you again!

Question 198364: This question has been confusing me and I really need some help. Thank You!
Find the solution of the system of equations by graphing.
y=-x+9
y=4x-1
Thank you again!
Found 2 solutions by arallie, jim_thompson5910:
Answer by arallie(162) (Show Source): You can put this solution on YOUR website!

Intersect at (2, 7)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Step 1) Graph

Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is

Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point

Now since the slope is comprised of the "rise" over the "run" this means

Also, because the slope is , this means:

which shows us that the rise is -1 and the run is 1. This means that to go from point to point, we can go down 1 and over 1

So starting at , go down 1 unit

and to the right 1 unit to get to the next point

Now draw a line through these points to graph

So this is the graph of through the points and

Step 2) Graph

Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is

Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point

Now since the slope is comprised of the "rise" over the "run" this means

Also, because the slope is , this means:

which shows us that the rise is 4 and the run is 1. This means that to go from point to point, we can go up 4 and over 1

So starting at , go up 4 units

and to the right 1 unit to get to the next point

Now draw a line through these points to graph

So this is the graph of through the points and

Step 3) Now graph and together on the same coordinate axis

Graph of (red) and (green)

From the graph, we see that the two lines intersect at the point (2,7)

So the solution to the system is and

This means that the system is independent and consistent.
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