1. **State the problem:** Solve the system of equations using elimination: $$\begin{cases} 3x + 10y = -4 \\ 2x + 2y = 2 \end{cases}$$ 2. **Explain the elimination method:** The goal is to eliminate one variable by making the coefficients of that variable equal (or opposites) in both equations, then subtract or add the equations. 3. **Make coefficients of $x$ equal:** Multiply the second equation by 3 and the first equation by 2 to get the same coefficient for $x$: $$\begin{cases} 2(3x + 10y) = 2(-4) \\ 3(2x + 2y) = 3(2) \end{cases}$$ which simplifies to $$\begin{cases} 6x + 20y = -8 \\ 6x + 6y = 6 \end{cases}$$ 4. **Subtract the second equation from the first to eliminate $x$:** $$ (6x + 20y) - (6x + 6y) = -8 - 6 $$ which simplifies to $$ 14y = -14 $$ 5. **Solve for $y$:** $$ y = \frac{-14}{14} = -1 $$ 6. **Substitute $y = -1$ into one of the original equations to find $x$:** Using the second equation: $$ 2x + 2(-1) = 2 $$ $$ 2x - 2 = 2 $$ $$ 2x = 4 $$ $$ x = 2 $$ 7. **Final answer:** The solution to the system is $$ (x, y) = (2, -1) $$ This means the lines intersect at the point $(2, -1)$ on the coordinate plane.