Using the following equation, what value of A$A$ makes the following system of equations have (-(4)/(7), -(1)/(7))$\left(-\frac{4}{7}, -\frac{1}{7}\right)$ as a solution? Ax + 5y = -3$Ax + 5y = -3$ -8x + Ay = 4$-8x + Ay = 4$

Related Formula

For y < mx + b$y < mx + b$, boundary is dashed, shading is below. For y ≥ mx + b$y \geq mx + b$, boundary is solid, shading is above.

Core Logic

Analyze boundary line 1: y = 2x + 4$y = 2x + 4$

• Dashed line with y-intercept (0, 4)$(0, 4)$ and positive slope 2$2$.
• y < 2x + 4$y < 2x + 4 \implies$ shade BELOW the dashed line.

Analyze boundary line 2: y = -(1)/(3)x - 2$y = -\frac{1}{3}x - 2$

• Solid line with y-intercept (0, -2)$(0, -2)$ and negative slope -(1)/(3)$-\frac{1}{3}$.
• y ≥ -(1)/(3)x - 2$y \geq -\frac{1}{3}x - 2 \implies$ shade ABOVE the solid line.

Step 1: Select Matching Graph

Graph A correctly shows shading above the solid line y = -(1)/(3)x - 2$y = -\frac{1}{3}x - 2$ and below the dashed line y = 2x + 4$y = 2x + 4$.

Hence, choice A is correct.

Pattern Recognition

Dashed vs. solid line test arrow$\rightarrow$ strict inequality (<$<$) requires dashed; non-strict (≥$\geq$) requires solid.

Chapter Mix

SAT Math: Heart of Algebra