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If 5x + 3y = 21 and 4x – y = 10, then x² + y² = ___. (A) 13 (B) 5 (C) 10 (D) 8

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Answer:

(A) 13

Explanation:

Step 1: Use the elimination method to solve for x:

  • Before we can find x^2 + y^2, we need to solve the system of equations.
  • We can start by multiplying the second equation by 3.

Doing so will allow us to eliminate y since 3y - 3y = 0:

3(4x - y = 10)

12x - 3y = 30

Step 2: Add 5x + 3y = 21 and 12x - 3y = 30 to eliminate y and solve for y:

Now we can add the second equation multiplied by 3 to the first equation to eliminate y and solve for x:

5x + 3y = 21

+

12x - 3y = 30

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(5x + 12x) + (3y - 3y) = (21 + 30)

(17x = 51) / 17

x = 3

Thus, x = 3.

Step 3: Plug in 3 for x in one of the equations to solve for y:

  • We can solve for y by plugging in 3 for x in any of the two equations.

Let's use the first equation (5x + 3y = 21):

5(3) + 3y = 21

(15 + 3y = 21) - 15

(3y = 6) / 3

y = 2

Thus, y = 2

Step 4: Evaluate x^2 + y^2 when x = 3 and y = 2:

Now we can find the final answer by plugging in 3 for x and 2 for y and simplifying:

Final answer = 3^2 + 2^2

Final answer = 9 + 4

Final answer = 13

Since x = 3 and y = 2, x^2 + y^2 = 13.

User Greg Robertson
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