Answer:
x=3, y=7
x=-2, y=2
Step-by-step explanation:
System of Equations
We have the following equations:
[tex]y=-x^2+2x+10[/tex]
[tex]y=x+4[/tex]
We'll solve it by substitution. Since the second equation is already solved for y, we use that expression and substitute into the first equation:
[tex]x+4=-x^2+2x+10[/tex]
Since this is a quadratic equation, it's convenient to have all terms to one side:
[tex]x+4+x^2-2x-10=0[/tex]
Simplifying and reordering:
[tex]x^2-x-6=0[/tex]
Factoring:
[tex](x-3)(x+2)=0[/tex]
Solving:
x=3, x=-2
Those yield to two solutions for y:
y=x+4
y=7, y=2
The solutions of the system are:
x=3, y=7
x=-2, y=2
