|
Question 47193: - Determine how many solutions exist
- Use either elimination or substitution to find the solutions (if any)
- Graph the two lines, labeling the x-intercepts, y-intercepts, and
points of intersection
y = 2x + 3 and y = -x - 4
Answer by tutorcecilia(2152)   (Show Source):
You can put this solution on YOUR website! - Determine how many solutions exist: One solution (-7/3, -5/3)
- Use the substitution method:
y = 2x + 3 and y = -x - 4 [Substitute one equation for "y"]
2x + 3 = -x - 4 [Solve for x]
2x+x+3=-x+x-4
3x+3-3=-4-3
3x=-7
3x/3=-7/3
x=-7/3
.
.
y = 2x + 3 [Plug-in (x=-7/3) back into one of the original equations]
y = 2(-7/3) + 3 [Solve for y]
y=-5/3
.
[Plug the values of x and y back into one of the original equations]
y = -x - 4
-5/3 = -(-7/3)-4
-1.66= -1.66 [Checks out]
.
- Graph the two lines, labeling the x-intercepts, y-intercepts, and
points of intersection:
Plot the following points and label on the graph:
y-intercept of y = 2x+3 = (0, 3)
x-intercept of y = 2x+3 = (-3/2, 0)
y-intercept of y = -x-4 = (0, -4)
x-intercpet of y = -x-4 = (-4, 0).
.
Points of intersection: (-7/3, -5/3)
|
|
|
| |
