1. The problem is to solve a linear equation in two variables using a table. 2. A linear equation in two variables generally has the form $ax + by = c$, where $a$, $b$, and $c$ are constants. 3. To solve it using a table, we select values for one variable (usually $x$), then calculate the corresponding values of the other variable ($y$) using the equation. 4. For example, consider the equation $2x + 3y = 6$. 5. Choose values for $x$: $x=0, 1, 2$. 6. Calculate $y$ for each $x$ using $y = \frac{6 - 2x}{3}$. 7. When $x=0$, $y = \frac{6 - 0}{3} = 2$. 8. When $x=1$, $y = \frac{6 - 2}{3} = \frac{4}{3}$. 9. When $x=2$, $y = \frac{6 - 4}{3} = \frac{2}{3}$. 10. The table of solutions is: | $x$ | $y$ | |-----|-----| | 0 | 2 | | 1 | $\frac{4}{3}$ | | 2 | $\frac{2}{3}$ | 11. These $(x,y)$ pairs satisfy the equation and represent points on the line defined by the equation. 12. This method helps visualize and understand the solutions of the linear equation.