To set up the expression 2x² + 4x + 8 as a system of equations, we first rewrite it as an equation by setting it equal to 0:
2x² + 4x + 8 = 0
Now this is a quadratic equation in standard form. To create a system, we can introduce another equation. A common approach is to pair this quadratic equation with a linear equation. For simplicity, let’s consider the linear equation:
y = 3
This gives us a constant value for y. Now, we can write our system of equations as follows:
- Equation 1: 2x² + 4x + 8 = 0
- Equation 2: y = 3
In this system, we now have one quadratic equation and one linear equation. Solving this system might involve finding the values of x from the quadratic equation and then substituting them into the second equation to find the corresponding y values. This way, we have effectively set up the expression as a system of equations.