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

STEP 1

1. We have two separate tasks: solve the equation $\frac{2}{5}y + \frac{3}{2}x = 1$ and evaluate the multiplication expression $\frac{3}{2} \times \frac{5}{2}$ .
2. The equation involves two variables, $x$ and $y$ , and cannot be solved for unique values without additional information.
3. The multiplication expression involves straightforward arithmetic with fractions.

STEP 2

1. Evaluate the multiplication expression $\frac{3}{2} \times \frac{5}{2}$ .
2. Discuss the equation $\frac{2}{5}y + \frac{3}{2}x = 1$ .

STEP 3

Evaluate the multiplication expression:
$\frac{3}{2} \times \frac{5}{2} = \frac{3 \times 5}{2 \times 2} = \frac{15}{4}$
The result of the multiplication is $\frac{15}{4}$ .

STEP 4

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 $y = \frac{5}{2} - \frac{15}{4}x$ .

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