Answer:
(-2, -31) and (-14.5, -37.25).
Step-by-step explanation:
The system of equations is
x² + 16x + y = -59
x - 2y = 60
To graph the system, we need to identify some points for each equation.
For the first equation, let's solve the equation for y
x² + 16x + y = -59
y = -x² - 16x - 59
The vertex of this equation occurs when x = -b/2a where b is the number beside x and a is the number besides x². So, in this case b = -16 and a = -1
x = -b/2a = -(-16)/2(-1) = 16/(-2) = -8
Then, if x = 0
y = -0² - 16(0) - 59
y = - 59
If x = -4
y = -(-4)² - 16(-4) - 59
y = -16 + 64 - 59
y = -11
If x = -8
y = -(-8)² - 16(-8) - 59
y = -64 + 128 - 59
y = 5
If x = -12
y = -(-12)² - 16(-12) - 59
y = -144 + 192 - 59
y = -11
Therefore, for the first equation, we will use the points (0, -59), (-4, -11), (-8, 5), and (-12, -11).
and the vertex of the parabola is (-8, 5)
For the second equation, we need two points, so
If x = 0
x - 2y = 60
0 - 2y = 60
-2y = 60
-2y/(-2) = 60/(-2)
y = -30
If x = -2
x - 2y = 60
-2 - 2y = 60
-2y = 60 + 2
-2y = 62
-2y/(-2) = 62/(-2)
y = -31
Therefore, we will graph the second graph using the points (0, -30) and (-2, -31)
Answer:
So, we can make the graph as
Then, the solutions are the points (-2, -31) and (-14.5, -37.25).