Respuesta :

sub x²+12x+30 for y

8x-y=10
8x-(x²+12x+30)=10
8x-x²-12x-30=10
-x²-4x-30=10
times -1 both sides
x²+4x+30=-10
add 10 both sides
x²+4x+40=0
factor
what 2 numbers multiply to get 40 and add to get 4?
none
ok, erm
how many real roots?
use discrimiant,
b²-4ac so
for ax²+bx+c=0
4²-4(1)(40)=16-160<0, no real roots

no solutions
lublana

Answer:

No solution

Step-by-step explanation:

We are given that two equations

[tex]y=x^2+12x+30[/tex]

[tex]8x-y=10[/tex]

We have to find the solutions of equations

Substitute the value of y in second equation

[tex]8x-(x^2+12x+30)=10[/tex]

[tex]8x-x^2-12x-30=10[/tex]

[tex]-x^2-4x-30-10=0[/tex]

[tex]-x^2-4x-40=0[/tex]

[tex]x^2+4x+40=0[/tex]

To find the nature of roots by finding discriminant

[tex]D=b^2-4ac[/tex]

[tex]D=4^2-4\times1\times 40=16-160=-144 <0[/tex]

Hence , no real roots exist .Therefore, no solution of the system of equations .

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