1. **Problem Statement:** Solve the system of linear equations: $$8x + 5y = 9$$ $$3x + 2y = 4$$ 2. **Method:** We will use the method of elimination to find $x$ and $y$. 3. **Step 1: Multiply equations to align coefficients of $y$:** Multiply the first equation by 2 and the second by 5 to make the coefficients of $y$ equal: $$2(8x + 5y) = 2(9) \Rightarrow 16x + 10y = 18$$ $$5(3x + 2y) = 5(4) \Rightarrow 15x + 10y = 20$$ 4. **Step 2: Subtract the second new equation from the first:** $$ (16x + 10y) - (15x + 10y) = 18 - 20 $$ $$ 16x - 15x + \cancel{10y} - \cancel{10y} = -2 $$ $$ x = -2 $$ 5. **Step 3: Substitute $x = -2$ into one of the original equations to find $y$:** Using the second original equation: $$3(-2) + 2y = 4$$ $$-6 + 2y = 4$$ $$2y = 4 + 6$$ $$2y = 10$$ $$\cancel{2}y = \cancel{2}5$$ $$y = 5$$ 6. **Final answer:** $$x = -2, \quad y = 5$$ This means the solution to the system is the point $(-2, 5)$ where both lines intersect.