1. An equation of the form $cx + dy = e$, where c and d are constants with d ≠ 0 and c ≠ 0, is known as a linear equation in two variables. Its solution represents a line with infinitely many points.
2. A system of linear equations consists of two or more linear equations. Specifically, a system of two linear equations in two variables can be expressed as:

3. A solution to a system of linear equations in two variables is the set of ordered pairs $(x, y)$ that simultaneously satisfy both equations.

i) $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$, indicates that the system has an infinite number of solutions

ii) $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$, indicates that the system has no solutions.

iii) $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$ indicates that the system has a unique (only one) solution.

4. Geometrically,

• If two lines intersect at a single point, the system has a unique solution.
• If two lines are parallel and do not intersect, the system has no solution.
• If two lines overlap completely, the system has infinitely many solutions.

5. A system of linear equations in two variables can be solved using one of the following methods: graphing, substitution, or elimination.