Certainly! Let's solve the equation \(2xy = 7\) step-by-step.
Understanding the Equation
The equation \(2xy = 7\) relates two variables, \(x\) and \(y\). Here, \(2\) is a coefficient, and the product of \(x\) and \(y\) is being multiplied by \(2\) to equal \(7\).
Isolating the Variables
To express this equation in terms of one variable, we can rearrange it:
- Divide both sides by \(2\):
\[
xy = \frac{7}{2}
\]
- From here, we can express \(y\) in terms of \(x\):
\[
y = \frac{7}{2x}
\]
Finding Solutions
This equation indicates that for any non-zero value of \(x\), you can find a corresponding value of \(y\):
- If \(x = 1\), then:
\[
y = \frac{7}{2 \cdot 1} = \frac{7}{2} = 3.5
\]
- If \(x = 2\), then:
\[
y = \frac{7}{2 \cdot 2} = \frac{7}{4} = 1.75
\]
- If \(x = -1\), then:
\[
y = \frac{7}{2 \cdot (-1)} = -\frac{7}{2} = -3.5
\]
Conclusion
The equation \(2xy = 7\) has infinitely many solutions depending on the value of \(x\). Each selected value of \(x\) yields a unique corresponding \(y\).
- Solutions can be represented as pairs \((x, y)\) such as:
- \((1, 3.5)\)
- \((2, 1.75)\)
- \((-1, -3.5)\)
This functional relationship illustrates how \(x\) and \(y\) are interdependent in this equation.