Solve the system of equations: $$\begin{cases} 3x + 2y = 5 \\ -5x + 2y = 45 \end{cases}$$

Solution Steps:

• Step 1: Subtract the second equation from the first equation to eliminate y.
• $$(3x + 2y) - (-5x + 2y) = 5 - 45$$
• $$3x + 2y + 5x - 2y = -40$$
• $$8x = -40$$
• Step 2: Solve for x.
• $$x = \frac{-40}{8}$$
• $$x = -5$$
• Step 3: Substitute the value of x into the first equation to solve for y.
• $$3(-5) + 2y = 5$$
• $$-15 + 2y = 5$$
• $$2y = 5 + 15$$
• $$2y = 20$$
• $$y = \frac{20}{2}$$
• $$y = 10$$

Final Answer: The solution is $$x = -5$$ and $$y = 10$$.