Solving Systems With Elimination

Explanation
The given answer (-4,3), (-4,3) is the solution to the system of equations x + 2y = 2 and -x + 3y = 13. When substituting x = -4 and y = 3 into both equations, we get the following: -4 + 2(3) = 2 which simplifies to -4 + 6 = 2, and -(-4) + 3(3) = 13 which simplifies to 4 + 9 = 13. Therefore, both equations are satisfied by the values x = -4 and y = 3, confirming that (-4,3), (-4,3) is the correct answer.

Explanation
The given answer (-3,-5),(-3, -5) is incorrect. The correct answer should be (-3, -5) because it satisfies both equations in the system. Substituting -3 for x and -5 for y in the first equation, we get -3(-3) + 10(-5) = 9 - 50 = -41, which is equal to the right-hand side of the equation. Similarly, substituting -3 for x and -5 for y in the second equation, we get 3(-3) - 5(-5) = -9 + 25 = 16, which is equal to the right-hand side of the equation. Therefore, (-3, -5) is the correct solution to the system.

Explanation
The given system of equations is 3x - 4y = -16 and x - 4y = -40. To solve this system, we can use the method of substitution. From the second equation, we can solve for x in terms of y: x = -40 + 4y. Substituting this value of x into the first equation, we get 3(-40 + 4y) - 4y = -16. Simplifying this equation, we get -120 + 12y - 4y = -16. Combining like terms, we get 8y = 104. Dividing both sides by 8, we get y = 13. Substituting this value of y into the second equation, we get x - 4(13) = -40. Simplifying this equation, we get x - 52 = -40. Adding 52 to both sides, we get x = 12. Therefore, the solution to the system is (12,13).