Please...I need help solving the following
system by graphing
x - 2y = 8
3x - 2y = 12
1. Find the x-intercept of the first equation,
by substituting y = 0 and solving for x
x - 2y = 8
x - 2(0) = 8
x = 8
So the x-intercept is the point (8,0) on
the x-axis
2. Find the y-intercept of the first equation,
by substituting
x = 0 and solving for y
x - 2y = 8
0 - 2y = 8
-2y = 8
y = -4
So the y-intercept is the point (0, -4) on
the y-axis.
Plot these two points and draw a line through them.
3. Find the x-intercept of the second equation,
by substituting y = 0 and solving for x
3x - 2y = 12
3x - 2(0) = 12
3x = 12
x = 4
So the x-intercept is the point (4,0) on the
x-axis
4. Find the y-intercept of the second equation,
by substituting x = 0 and solving for x
3x - 2y = 12
3(0) - 2y = 12
-2y = 12
y = -6
So the y-intercept is the point (0, -6) on the
y-axis.
Plot these two points and draw a line through them
on the same set of axes.
Now look and see what the coordinates are of the point
where the two lines cross:
You will notice that point is directly under 2 on the
x-axis, and it's directly to the right of -3 on the
y-axis. So the solution of the system is
(x,y) = (2,-3)
We can check that to see if it is correct. Substitute
x=2 and y=-3 into both of the original equations and
see if you end up with the same number on both sides.
x - 2y = 8 3x - 2y = 12
(2) - 2(-3) = 8 3(2) - 2(-3) = 12
2 + 6 = 8 6 + 6 = 12
8 = 8 12 = 12
It checks in both.
Edwin
