Question

Y=x^2+12x+30 8x-y=10

Answer 1

y = x² + 12x + 30
8x - y = 10

8x - y = 10
- 8x - 8x
-y = -8x + 10
-1 -1
y = 8x - 10

x² + 12x + 30 = 8x - 10
- 8x - 8x
x² + 4x + 30 = -10
- 10 - 10
x² + 4x + 20 = 0
x = -b ± √b² - 4ac
2a
x = -4 ± √4² - 4(1)(20)
2(1)
x = -4 ± √16 - 4(20)
2
x = -4 ± √16 - 80
2
x = -4 ± √-64
2
x = -4 ± 8i
2
x = -2 ± 4i

Answer 2

y=x^2+12x+30
8x-y=10
sub x^2+12x+30 for y in the secodn equaiton

8x-(x^2+12x+30)=10
8x-x^2-12x-30=10
-x^2-4x-30=10
times -1
x^2+4x+30=-10
add 10 both sides
x^2+4x+40=0
use quadratic formula
we find that we have 2 imaginary roots and therefor are not on the real plane, they are not plotted on the imaginary plane

no real solution
x=-2+6i or -2-6i
the interseciton on the imaginary plane is
(-2+6i, -26+48i) or (-2-6i,-26-48i)