Question

Solve the system by substitution.
y=-x^2+2x+10
y=x+4

Answer 1

x=3, y=7

x=-2, y=2

Explanation:

System of Equations

We have the following equations:

`y=-x^2+2x+10`

`y=x+4`

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:

`x+4=-x^2+2x+10`

Since this is a quadratic equation, it's convenient to have all terms to one side:

`x+4+x^2-2x-10=0`

Simplifying and reordering:

`x^2-x-6=0`

Factoring:

`(x-3)(x+2)=0`

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