1. Let's understand why we multiply by $-2$ in certain problems. 2. Often, multiplying by $-2$ is used to eliminate a variable or to simplify an equation. 3. For example, if you have an equation like $x + 2y = 6$ and another like $3x - y = 4$, multiplying the second equation by $-2$ helps align coefficients for elimination: $$3x - y = 4 \implies -2(3x - y) = -2(4)$$ 4. This gives: $$-6x + 2y = -8$$ 5. Now, adding this to the first equation: $$x + 2y = 6$$ $$-6x + 2y = -8$$ 6. Adding both: $$x - 6x + 2y + 2y = 6 - 8$$ $$-5x + 4y = -2$$ 7. The multiplication by $-2$ was to create opposite coefficients for $y$ to eliminate it or to simplify the system. 8. So, multiplying by $-2$ is a strategic step to make solving easier by canceling terms. This is a common technique in solving systems of equations.