Question

Solve this nonlinear system of equations. Show your work.Y= -x^2 + 6x - 5 Y=3 A. Use substitution to combine equations. Rewrite so that one side is equal to 0.

Answer 1

Substitute the value of y of the second equation into the value of y in the first equation.

`3=-x^2+6x-5`

Equate the expression to 0 by adding x² and 5 and subtracting 6x from both sides of the equation.

`\begin{gathered} x^2-6x+5+3=0 \\ x^2-6x+8=0 \end{gathered}`

Factor the left side of the equation.

`(x-2)(x-4)=0`

Equate each factor to 0 and then solve for x.

`\begin{gathered} x-2=0 \\ x=2 \\ \\ x-4=0 \\ x=4 \end{gathered}`

Thus, the equations intersect at

`(2,3)\text{ and }(4,3)`