1. **State the problem:** We need to identify the system of linear equations from the graph description. 2. **Analyze the graph:** One line passes through the origin with a positive slope, and the other line has a negative slope with a y-intercept at -5. 3. **Recall the slope-intercept form:** The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 4. **Identify the positive slope line:** Since it passes through the origin, its y-intercept $b=0$. The slope is positive and could be $\frac{2}{3}$ or $\frac{3}{4}$. 5. **Identify the negative slope line:** It has a y-intercept at $-5$ and a negative slope, which must be the negative of the other fraction. 6. **Check each option:** - Option A: $y=\frac{2}{3}x$ (positive slope, passes origin), $y=-\frac{3}{4}x - 5$ (negative slope, intercept -5) matches the description. - Option B: Positive slope is $-\frac{2}{3}$ (negative), so no. - Option C: Positive slope $\frac{3}{4}$ but negative slope $-\frac{2}{3}$ with intercept -5, but positive slope line passes origin, so possible. - Option D: Positive slope is $-\frac{3}{4}$ (negative), no. 7. **Compare slopes:** The positive slope line passes through origin, so its equation must have $b=0$. Both A and C satisfy this. 8. **Check which negative slope matches the positive slope's reciprocal:** The slopes are $\frac{2}{3}$ and $-\frac{3}{4}$ in A, and $\frac{3}{4}$ and $-\frac{2}{3}$ in C. 9. **Since the problem states the slopes correspond to fractions $\frac{2}{3}$ or $\frac{3}{4}$ and their negatives, and the negative slope line crosses y-axis at -5, option A fits best.** **Final answer:** $$\begin{cases} y = \frac{2}{3}x \\ y = -\frac{3}{4}x - 5 \end{cases}$$