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Question 132186This question is from textbook Algebra
: find a common solution for each system of equations:
y=3x+5
y=-5x-3
This question is from textbook Algebra
Found 2 solutions by nycsharkman, jim_thompson5910:
Answer by nycsharkman(136)   (Show Source):
You can put this solution on YOUR website! The best way to find a solution in this example is to graph both linear equations on the SAME coordinate system (graph paper). The solution for this system will be the point where the two graphs meet.
I assume you know how to graph linear equations, right?
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website! First let's 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 3 and the run is 1. This means that to go from point to point, we can go up 3 and over 1
So starting at , go up 3 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
Now let's 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 -5 and the run is 1. This means that to go from point to point, we can go down 5 and over 1
So starting at , go down 5 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
If we graph the two equations on the same coordinate system, we can see that the two lines intersect at the point (-1,2)
 Graph of (red) and (green) which intersect at the point (-1,2)
So the common solution is
 and 
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