Question

What terms can eliminate themselves?
For example:
3x + _____ would eliminate to 0.

Answer 1

How many equations do we need for solving if we have 2 variables?

Answer 2

To eliminate terms in expression simplification, you're looking for expressions that equal zero when added together with a given term.

In your example, the term \( 3x \) would be eliminated if you add \( -3x \) (or \( -1 \times 3x \)). Therefore, you could fill in the blank with:

- **-3x**

So, \( 3x + (-3x) = 0 \).

In general, for any term \( ax \), the term that would eliminate it would be \( -ax \).

Answer 3

To solve a system of equations with 2 variables, you typically need 2 equations. This is because:

1. **Single Equation**: One equation can represent a line in a two-dimensional plane, resulting in infinitely many solutions (unless it is a special case, like a vertical line or a constant).

2. **Two Equations**: Two equations can intersect at a single point (which represents a unique solution), be parallel (no solution), or be the same line (infinitely many solutions).

So, to find a unique solution for 2 variables, you need 2 equations.