Question

6) 5(x + y) - 7(x - y) = 10, 4(x + y) + 3(x - y) = 51.

Answer 1

Ответ:

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Объяснение:

Answer 2

To solve this system of equations:

1. Start by simplifying both equations:

   Equation 1: 5(x + y) - 7(x - y) = 10 Equation 2: 4(x + y) + 3(x - y) = 51

2. Distribute the constants to the terms inside the parentheses:

   Equation 1: 5x + 5y - 7x + 7y = 10 Equation 2: 4x + 4y + 3x - 3y = 51

3. Combine like terms on both sides of the equations:

   Equation 1: -2x + 12y = 10 Equation 2: 7x + y = 51

4. You now have a system of two equations with two variables:

   -2x + 12y = 10 7x + y = 51

5. You can use either the substitution method or the elimination method to solve for x and y. I'll use the elimination method in this example.

   First, multiply the second equation by 2 to make the coefficients of y in both equations cancel each other out:

   -2x + 12y = 10 14x + 2y = 102

6. Now, you can add the two equations together to eliminate y:

   (-2x + 12y) + (14x + 2y) = 10 + 102 12x + 14y = 112

7. Divide the entire equation by 2 to simplify it further:

   6x + 7y = 56

8. Now, you have a new equation:

   6x + 7y = 56

9. You have a system of two equations:

   -2x + 12y = 10 6x + 7y = 56

10. Solve this system of equations simultaneously. Let's multiply the first equation by 3 to make it easier to eliminate x:

-6x + 36y = 30 6x + 7y = 56

11. Add the two equations:

(-6x + 36y) + (6x + 7y) = 30 + 56 43y = 86

12. Divide both sides by 43 to solve for y:

y = 86 / 43 y = 2

13. Now that you know the value of y, you can substitute it back into one of the original equations to solve for x. Let's use Equation 2:

7x + 2 = 51

14. Subtract 2 from both sides:

7x = 49

15. Divide both sides by 7 to solve for x:

x = 49 / 7 x = 7

So, the solution to the system of equations is:

x = 7 y = 2