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.