How can x² + 3x + 1 + 2x² + 2x + 3 be set up as a system of equations?

To convert the expression x² + 3x + 1 + 2x² + 2x + 3 into a system of equations, we first need to simplify the expression.

Combine like terms:

• The x² terms: x² + 2x² = 3x²
• The x terms: 3x + 2x = 5x
• The constant terms: 1 + 3 = 4

So, the simplified expression is:

3x² + 5x + 4 = 0

This single equation can be set up as a system by assigning it the label ‘Equation 1’. However, to create a full system, we usually need a second equation. Here’s an example of how you might construct a second equation:

Let’s say we want to relate x to another variable, y. We can introduce a simple linear equation:

y = 2x + 1

Now, we have a system of equations:

Equation 1: 3x² + 5x + 4 = 0
Equation 2: y = 2x + 1

This system can be solved simultaneously for x and y, allowing us to find values that satisfy both equations.