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beks73
1 month ago
6

PART D

Physics
1 answer:
ValentinkaMS [3.4K]1 month ago
5 0

Answer:

Solution:

  • D = -4/7
  • C = 17/7

Explanation:

To solve the system via substitution, proceed as follows:

  • 1. Choose the variable with the smallest coefficient and isolate it on one side.
  • 2. Divide both sides by that variable's coefficient.
  • 3. Substitute this expression into the other equation.
  • 4. Solve for the remaining variable.

Applying these steps to the system:

  • 3C + 4D = 5
  • 2C + 5D = 2

Step 1: Isolate the variable with the smaller coefficient:

  • 2C = 2 - 5D

Step 2: Divide both sides by 2

  • C = (2 - 5D)/2

Step 3: Substitute into the first equation

  • 3 * (2 - 5D)/2 + 4D = 5

Step 4: Solve the equation

  • Apply distributive property: multiply 3 by each term inside the parentheses

(6 - 15D)/2 + 4D = 5

  • Divide each term within the parentheses by 2:

3 - (15D)/2 + 4D = 5

  • Move 3 to the right side by subtracting:

-(15D)/2 + 4D = 5 - 3

  • Combine like terms:

(-15D + 8D) / 2 = 2

-7D = 4

D = -4/7

  • Plug D back into the equation for C:

 

C = (2 - 5D)/2 = (2 - 5(-4/7))/2

C = (2 + 20/7)/2

C = (14/7 + 20/7)/2

C = 34/7 / 2

C = 34/14

C = 17/7

Final solution:

  • D = -4/7
  • C = 17/7
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