Questions: Which ordered pair is a solution of the given system? 2x + 5y = -11 10x + 3y = 11 A. (3,-2) B. (-3,2) C. (2,-3) D. (-2,3)

Transcript text: Which ordered pair is a solution of the given system? \[ \begin{array}{l} 2 x+5 y=-11 \\ 10 x+3 y=11 \end{array} \] A. $(3,-2)$ B. $(-3,2)$ C. $(2,-3)$ D. $(-2,3)$

Solution

Solution Steps

Step 1: Substitute the first ordered pair into the system

Substitute $ (3, -2) $ into the first equation: \[ 2(3) + 5(-2) = 6 - 10 = -4 \neq -11 \] Since this does not satisfy the first equation, $ (3, -2) $ is not a solution.

Step 2: Substitute the second ordered pair into the system

Substitute $ (-3, 2) $ into the first equation: \[ 2(-3) + 5(2) = -6 + 10 = 4 \neq -11 \] Since this does not satisfy the first equation, $ (-3, 2) $ is not a solution.

Step 3: Substitute the third ordered pair into the system

Substitute $ (2, -3) $ into the first equation: \[ 2(2) + 5(-3) = 4 - 15 = -11 \] This satisfies the first equation. Now check the second equation: \[ 10(2) + 3(-3) = 20 - 9 = 11 \] This also satisfies the second equation. Therefore, $ (2, -3) $ is a solution.

Final Answer

$\boxed{(2, -3)}$

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