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What does it mean to solve a system of equations by graphing?
What you are being asked to do is graph each equation and then note the point at which they intersect. This intersection is the solution for the system.
To begin with write each equation in slope intercept form.
Slope intercept form is:
y = mx + b
m is the slope of the line
and b is the y intercept (the point at which the line crosses the y axis)
So lets look at the first equation
2x - y = 4
move 2x to the right side of the equation
to do this subtract 2x from both sides
2x - 2x - y = -2x + 4
-y = -2x + 4
next get rid of the negative sign in front of the y
to do this divide both sides by -1
-y/-1 = -2x/-1 + 4/-1
y = 2x - 4
Ok now we have this equation in slope intercept form
the slope is 2
and the y intercept is -4
Lets graph the line
start at the y intercept -4
Place a dot on your graph at point (0,-4)
Now slope is defined as
since the slope for this line is 2 which is equal to
the rise is 2 and the run is 1
Starting at the y intercept point (0,-4) we are going to use the slope to
find the next point on this line
So place your pencil at point (0,-4) on the graph
now rise up 2
your pencil should be at point (0,-2) on the graph
now run to the right 1
Now your pencil should be at point (1,-2) mark a dot here
Ok now use a ruler to draw a line through both points
Your graph should now look like this:
Ok now follow these same steps to graph the second equation
2x - y = 6
2x - 2x - y = -2x + 6
-y = -2x + 6
-y/-1 = -2x/-1 + 6/-1
y = 2x - 6
slope for this line is 2 or
y intercept is -6
Graph it following the same steps as before
only this time the starting point is (0,-6) because that is the y intercept for this line
Now the graph contains both lines:
So looking at the graph we can see that the lines are parallel.
There is no point of intersection.
This means there are no solutions, and the system is called inconsistent.