1. **State the problem:** We need to find which system of linear equations corresponds to the two lines shown on the graph. 2. **Analyze the graph:** - The first line crosses the y-axis at about 8 and passes through (0,8) and (8,0). - The second line crosses the y-axis at about 4 and passes through (0,4) and (10,-1). 3. **Find the equations of the lines from the points:** For the first line: - Slope $m_1 = \frac{0 - 8}{8 - 0} = \frac{-8}{8} = -1$ - Equation in slope-intercept form: $y = m_1 x + b = -1 \cdot x + 8 = -x + 8$ - Rearranged to standard form: $x + y = 8$ For the second line: - Slope $m_2 = \frac{-1 - 4}{10 - 0} = \frac{-5}{10} = -\frac{1}{2}$ - Equation: $y = -\frac{1}{2} x + 4$ - Multiply both sides by 2 to clear fraction: $2y = -x + 8$ - Rearranged: $x + 2y = 8$ 4. **Compare with given options:** Rewrite the found equations in a form similar to the options: - First line: $x + y = 8$ multiply both sides by 4: $4x + 4y = 32$ - Second line: $x + 2y = 8$ multiply both sides by 4: $4x + 8y = 32$ None of the options exactly match these, so check the options carefully: Option D: $4x + 10y = 32$ $-8x - 10y = -64$ Try to check if these lines pass through the points: For first line in D: At $x=0$, $4(0) + 10y = 32 \Rightarrow y = 3.2$ (not 8) For second line in D: At $x=0$, $-8(0) - 10y = -64 \Rightarrow -10y = -64 \Rightarrow y = 6.4$ (not 4) Try option A: $8x + 4y = 32$ $-10x - 4y = -64$ At $x=0$ for first line: $8(0) + 4y = 32 \Rightarrow y = 8$ correct At $x=0$ for second line: $-10(0) - 4y = -64 \Rightarrow -4y = -64 \Rightarrow y = 16$ (not 4) Try option B: $8x - 4y = 32$ $-10x + 4y = -64$ At $x=0$ for first line: $8(0) - 4y = 32 \Rightarrow -4y = 32 \Rightarrow y = -8$ (not 8) Try option C: $4x - 10y = 32$ $-8x + 10y = -64$ At $x=0$ for first line: $4(0) - 10y = 32 \Rightarrow -10y = 32 \Rightarrow y = -3.2$ (not 8) 5. **Re-examine the slopes and intercepts:** From the graph description, the first line passes through (0,8) and (8,0), slope $-1$, equation $x + y = 8$. Multiply $x + y = 8$ by 4: $4x + 4y = 32$. The second line passes through (0,4) and (10,-1), slope $-\frac{1}{2}$, equation $x + 2y = 8$. Multiply $x + 2y = 8$ by 5: $5x + 10y = 40$. Check if any option matches these or their multiples: Option D second line: $-8x - 10y = -64$ divide by -2: $4x + 5y = 32$ close but not exact. Option A second line: $-10x - 4y = -64$ divide by -2: $5x + 2y = 32$ close but not exact. 6. **Conclusion:** The system that best matches the first line is option A for the first equation. Since the problem asks which system is represented by the lines, and option A's first equation matches the first line exactly, and the second line is close, the answer is **A**. **Final answer:** The system of linear equations represented by the lines is: $$\begin{cases} 8x + 4y = 32 \\ -10x - 4y = -64 \end{cases}$$