Final answer:
To solve the system of equations 6x + 3y = 24 and -2x + y = 20, you can use the method of substitution. The solution to the system is x = -3 and y = 14.
Step-by-step explanation:
To solve the system of equations: 6x + 3y = 24 and -2x + y = 20, we can use the method of substitution or elimination. Let's use substitution: Starting with the second equation, we solve it for y: -2x + y = 20, add 2x to both sides, and we get y = 2x + 20. Now we substitute this expression for y in the first equation: 6x + 3(2x + 20) = 24. Simplifying this equation, we get 6x + 6x + 60 = 24. Combining like terms, we have 12x + 60 = 24. Subtracting 60 from both sides, we get 12x = -36. Finally, by dividing both sides by 12, we find that x = -3. Now we substitute this value of x back into the second equation: -2(-3) + y = 20. Simplifying, we have 6 + y = 20. Subtracting 6 from both sides, we find y = 14. Therefore, the solution to the system of equations is x = -3 and y = 14.