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Use the substitution method to solve the system of equations. Choose the correct ordered pair.2x + 2y = 16y = x – 4A.(6, 2)B.(2, –2)C.(2, 2)D.(6, –2)

Question

Use the substitution method to solve the system of equations. Choose the correct ordered pair.

2x+2y=16 2x + 2y = 16 y=x−4 y = x - 4

A. (6, 2)
B. (2, –2)
C. (2, 2)
D. (6, –2)

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Solution

Step 1: We are given that y = x - 4.

Step 2: Substitute y = x - 4 into the other equation, 2x + 2y = 16.

This gives us 2x + 2(x - 4) = 16.

Step 3: Simplify the equation.

This gives us 2x + 2x - 8 = 16.

Step 4: Combine like terms.

This gives us 4x - 8 = 16.

Step 5: Add 8 to both sides of the equation.

This gives us 4x = 24.

Step 6: Divide both sides by 4.

This gives us x = 6.

Step 7: Substitute x = 6 into the equation y = x - 4.

This gives us y = 6 - 4 = 2.

So, the solution to the system of equations is (6, 2), which corresponds to option A.

This problem has been solved

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