Use graphing to find the solutions to the system of equations.
y = x2 + 6x + 8 and y = x + 4
Solution:
Given equations are y = x2 + 6x + 8 and y = x + 4
as mentioned, we shall use graph technique to find the solution
First,let’s take sample values of x, y
Let y1 = x2 + 6x + 8 and y2 = x + 4
| x | -5 | -3 | -1 | 0 | 1 | 3 | 5 |
|---|---|---|---|---|---|---|---|
| y1 | 3 | -1 | 3 | 8 | 23 | 35 | 63 |
| y2 | -1 | 1 | 3 | 4 | 5 | 7 | 9 |
We can graphically solve as follows:
Here, the horizontal axis is x-axis and the vertical axis is y-axis
Since, the straight line cuts the parabola at two different points, we will have 2 intersection points.
The intersection point of the two graphs can be calculated as
x + 4 = x2 + 6x + 8
⇒ x2 + 6x + 8 - x - 4 = 0
⇒ x2 + 5x +4 = 0
⇒ x2 + x + 4x + 4 = 0
⇒ x(x + 1) + 4(x + 1) = 0
⇒ (x + 4)(x + 1) = 0
⇒ x = -1, -4
Put x = -1 in y = x + 4, we get y = 3, so, (x, y) =(-1, 3)
Put x = -4 in y = x + 4, we get y = 0, so, (x,y) =(-4, 0)
Therefore, the solution set are (-1, 3) and (-4, 0)
Use graphing to find the solutions to the system of equations.
y = x2 + 6x + 8 and y = x + 4
Summary:
The solutions to the system of equations y = x2 + 6x + 8 and y = x + 4 are (-1, 3) and (-4, 0)