Question2. $\begin{array}{l}\frac{2}{5} y \frac{+3}{2} x=1 \quad \frac{3}{2} \times \frac{5}{2} \\ \quad \frac{2}{=} y \stackrel{+3}{2} x=1\end{array}$

Studdy Solution
Discuss the equation $\frac{2}{5}y + \frac{3}{2}x = 1$:
Since this is a linear equation with two variables, it represents a line in the $xy$-plane. Without additional constraints or a second equation, we cannot solve for unique values of $x$ and $y$. However, we can express one variable in terms of the other.
For example, solving for $y$ in terms of $x$:
$$\frac{2}{5}y = 1 - \frac{3}{2}x$$
Multiply both sides by $\frac{5}{2}$ to isolate $y$:
$$y = \frac{5}{2} \left( 1 - \frac{3}{2}x \right)$$
$$y = \frac{5}{2} - \frac{15}{4}x$$
This equation expresses $y$ in terms of $x$.
The multiplication result is $\frac{15}{4}$, and the equation $\frac{2}{5}y + \frac{3}{2}x = 1$ can be expressed as $y = \frac{5}{2} - \frac{15}{4}x$.