1. **Stating the problem:** We have the system of equations: $$3x - 2y = a$$ $$ax + by = 10$$ with the solution $x = -2$ and $y = -1$. We need to find the values of $a$ and $b$. 2. **Substitute the solution into the first equation:** $$3(-2) - 2(-1) = a$$ $$-6 + 2 = a$$ $$a = -4$$ 3. **Substitute the solution and $a$ into the second equation:** $$(-4)(-2) + b(-1) = 10$$ $$8 - b = 10$$ 4. **Solve for $b$:** $$8 - b = 10$$ $$-b = 10 - 8$$ $$-b = 2$$ $$b = -2$$ 5. **Final answer:** $$a = -4, \quad b = -2$$ --- **b) Solve the system graphically:** The system is: $$3x - 2y = -4$$ $$-4x - 2y = 10$$ Rewrite each equation in slope-intercept form $y = mx + c$: For the first equation: $$3x - 2y = -4$$ $$-2y = -3x - 4$$ $$y = \frac{3}{2}x + 2$$ For the second equation: $$-4x - 2y = 10$$ $$-2y = 4x + 10$$ $$y = -2x - 5$$ Plotting these two lines will show their intersection point. Using a graphing tool, the intersection point is approximately: $$x = -2.00, \quad y = -1.00$$ This matches the given solution. --- **Summary:** - $a = -4$ - $b = -2$ - Graphical solution confirms $x = -2.00$, $y = -1.00$