Answer:
Correct choice: B
Step-by-step explanation:
System of non-linear equations
It's given the following system of equations:
[tex]y=x^2+3x+5[/tex]
[tex]y=x+13[/tex]
We'll use the substitution method. Substituting y from the first equation into the second equation, we have:
[tex]x^2+3x+5=x+13[/tex]
Moving all terms to the left side:
[tex]x^2+3x+5-x-13=0[/tex]
Simplifying:
[tex]x^2+2x-8=0[/tex]
Factoring:
[tex](x+4)(x-2)=0[/tex]
There are two solutions:
x=-4, x=2
The first solution gives a value for y:
y=-4+13=9
First solution: (-4,9)
The second solution gives a value for y:
y=2+13=15
Second solution: (2,15)
Correct choice: B
