Question

solve this nonlinear system of equations.
y=-x^2+6x-5
y=3
step 1: use substitution to combine the equations. Rewrite so that one side is equal to zero.
step 2: factor the equation
step 3: identify the x-values of the solutions.
step 4: identify the solutions to the system.

Answer 1

Answer:

1. $x^2-6x+8=0$

2. $(x-4)(x-2)=0$

3. $x=4 \text{ and } x=2$

4. $x=4 \text{ and } x=2$

Step-by-step explanation:

1. When using substitution all we do would be is substituse the y for a 3.

This leaves us with the equation:

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

Rewriting it we get:
$0=-x^2+6x-8$

or if we shift the 0 to the other side:

$x^2-6x+8=0$

2. In order to factor the equation we can use the butterfly method:

$\left[\begin{array}{ccc}1&-4\\1&-2\end{array}\right]$
So it factors out to:

$(x-4)(x-2)=0$
You can also use the quadratic formula.

3. To find the solutions we just set each factor to 0
$x-4=0\\\text{and}\\x-2=0$
So the x-values would be:
$x=4 \text{ and } x=2$

4. To find the solution to the system we just plug in the values and it turns out to be the same numbers as before.