Hi, can someone please help me solve the following by
graphing? Thanks in advance!
1. 3x - 5y = -9
5x - 6y = -8
Get some points on the first line:
(-8,-3), (-3,0), and (7,6), plot them and draw
a red line through them:
Get some points on the second line:
(-10,-7), (-4,-2), and (8,8), plot them and draw
a green line through them:
Now we have to guess where the two lines intersect. To do this
draw a blue vertical line through the point of intersection:
Notice that it crosses the x-axis at 2, so the x coordinate of the
point of intersection is 2.
Now draw a horizontal line through the point of intersection:
Notice that it crosses the y-axis at 3, so the y coordinate of the
point of intersection is 3.
So the solution is (x,y) = (2,3)
Check substitute 2 for x and 3 for y in both original equations:
3x - 5y = -9
5x - 6y = -8
3(2) - 5(3) = -9
5(2) - 6(3) = -8
6 - 15 = -9
10 - 18 = -8
-9 = -9
-8 = -8
It checks.
2. 4x + 5y = -2
4y - x = 11
Get some points on the first line:
(-8,6), (2,-2), and (7,-6), plot them and draw
a red line through them:
Get some points on the second line:
(-7,1), (5,4), and (9,5), plot them and draw
a green line through them:
Now we have to guess where the two lines intersect. To do this
draw a blue vertical line through the point of intersection:
Notice that it crosses the x-axis at -3, so the x coordinate of the
point of intersection is -3.
Now draw a horizontal line through the point of intersection:
Notice that it crosses the y-axis at 2, so the y coordinate of the
point of intersection is 2.
So the solution is (x,y) = (-3,2)
Check substitute -3 for x and 2 for y in both original equations:
2. 4x + 5y = -2
4y - x = 11
4(-3) + 5(2) = -2
4(2) - (-3) = 11
-12 + 10 = -2
8 + 3 = 11
-2 = -2
11 = 11
It checks.
Edwin
