Question

What is the best approximation of the solution to the system to the nearest integer values? Responses (7, −2) begin ordered pair 7 comma negative 2 end ordered pair (−2, 6) begin ordered pair negative 2 comma 6 end ordered pair (6, −2) begin ordered pair 6 comma negative 2 end ordered pair (−2, 7) begin ordered pair negative 2 comma 7 end ordered pair Graph of a system of linear equations. Equation 1 is 3 x minus 4 y equals negative 32. Equation 2 is 3 x plus 5 y equals 24.

Answer 1

(b) (-2, 6)

Explanation:

You want the best integer approximation of the solution to the system of equations ...

• 3x -4y = -32
• 3x +5y = 24

Solution

Subtracting the first equation from the second, we have ...

(3x +5y) -(3x -4y) = (24) -(-32)

9y = 56

y = 56/9 = 6 2/9 ≈ 6

This tells us the best answer choice is ...

(x, y) ≈ (-2, 6) . . . . . . choice B

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Additional comment

Since the answer choices differ in their y-values, we do not need to know the value of x to make the correct selection. We could find x to be ...

x = (-32 +4(56/9))/3 = -64/27 = -2 10/27 ≈ -2 . . . . . matches choice B

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