To convert the expression x4 + 3x – 12 into a system of equations, we first need to isolate the variable and create relationships between multiple equations. The expressions can represent a function, and by setting it equal to zero, we can treat it as an equation:
1. First, we start by rewriting the equation:
x4 + 3x – 12 = 0
2. To set it up as a system of equations, we can introduce a substitution. Let’s say we want to express x4 in terms of other variables. One common method is to set:
- y = x4
- z = 3x
3. Then, we can rewrite our original equation using y and z:
y + z – 12 = 0
4. Thus, we have the following system of equations:
- y = x4
- z = 3x
- y + z – 12 = 0
This system allows us to explore the relationships between these variables and leads us toward finding the solutions by substituting back to find x. This approach transforms a polynomial expression into a more manageable set of linear relationships, enabling easier solution-finding through methods like substitution or elimination.