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practice examMultiple Choice

Practice Exam

Question 1 • Mathematics I

The table can be used to determine the solution to the system of equations, 2 x minus 2 y is equal to 6 and 4 x plus 4 y is equal to 28 Original System Equivalent System Sum of Equations in Equivalent System Solution to System New System using Sum Solution to New System 2 x minus 2 y is equal 6; 4 x plus 4 y is equal to 28 4 x minus 4 y is equal 12; 4 x plus 4 y is equal to 28 8 x is equal to 40 4 x plus 4 y is equal to 28; 8 x is equal to 40 Which solution can be used to fill in both blanks in the table?

Answer
A
2 comma 5
B
5 comma 2
C
5 comma negative 8
D
negative 8 comma 5

Explanation

Adding the equivalent equations, 4x − 4y = 12 and 4x + 4y = 28, cancels the y-terms and gives 8x = 40, so x = 5. Substitute x = 5 into 4x + 4y = 28: 20 + 4y = 28, so y = 2. The solution is (5, 2), choice B.

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