1. **State the problem:** Solve the system of linear equations: $$-8x + 4y = -24$$ $$-7x + 4y = -16$$ 2. **Method:** We will use the elimination method to solve for $x$ and $y$. 3. **Step 1: Subtract the second equation from the first to eliminate $y$:** $$(-8x + 4y) - (-7x + 4y) = -24 - (-16)$$ Simplify: $$-8x + 4y + 7x - 4y = -24 + 16$$ $$(-8x + 7x) + (4y - 4y) = -8$$ $$-x + 0 = -8$$ So, $$-x = -8$$ 4. **Step 2: Solve for $x$:** $$x = 8$$ 5. **Step 3: Substitute $x=8$ into one of the original equations to find $y$. Use the first equation:** $$-8(8) + 4y = -24$$ Simplify: $$-64 + 4y = -24$$ 6. **Step 4: Solve for $y$:** Add 64 to both sides: $$4y = -24 + 64$$ $$4y = 40$$ Divide both sides by 4: $$\cancel{4}y = \cancel{4}10$$ $$y = 10$$ 7. **Final answer:** $$x = 8, \quad y = 10$$