Solve the system by graphing.
x - 2y = 8
x + y = -1
Let's graph the first one by finding a couple of points:
Arbitrarily pick a letter, say y, and arbitrarily pick a
number to substitute for it, say, -1. So
x - 2y = 8 becomes
x - 2(-1) = 8
x + 2 = 8
x = 6
So we have the point (x,y) = (6,-1)
Now arbitrarily pick a letter, say x, and arbitrarily pick
another number to substitute for it, say, 4. So
x - 2y = 8 becomes
4 - 2y = 8
-2y = 4
y = -2
So we have the point (x,y) = (4,-2)
Now we can graph the first line by plotting those two points
and drawing a line through them:
Now let's graph the second one by finding a couple of points:
Arbitrarily pick a letter, say x, and arbitrarily pick a
number to substitute for it, say, 0. So
x + y = -1 becomes
0 + y = -1
y = -1
So we have the point (x,y) = (0,-1)
Now arbitrarily pick a letter, say x, and arbitrarily pick
another number to substitute for it, say, 4. So
x + y = -1 becomes
4 + y = -1
y = -5
So we have the point (x,y) = (4,-5)
Now we can graph the second line by plotting those two points
and drawing a line through them:
The object is to find the coordinates of the point where they
cross. Let's draw both a horizontal line and a vertical line
through the point where they cross:
Notice that the vertical line cuts the x-axis at 2 and that the
horizontal line cuts the y-axis at -3.
So the solution is (x,y) = (2,-3)
Now let's check to see if we are correct by substituting 2 for
x and -3 for y in both equations:
Substituting in the first:
x - 2y = 8
2 - 2(-3) = 8
2 + 6 = 8
8 = 8
That checks.
Substituting in the second:
x + y = -1
2 + (-3) = -1
2 - 3 = -1
-1 = -1
That checks. So we know the solution is
(x,y) = (2,-3) or x = 2 and y = -3
Edwin
