Question

If 2x + 2y = 2 and 3x - y = 7, which of the following ordered pairs (x, y) satisfies both equations?

(A) (1, 0)
(B) (2, 1)
(C) (3, 2)
(D) (4, 3)

Answer 1

The correct ordered pair (x, y) that satisfies both equations 2x + 2y = 2 and 3x - y = 7 is (1, 0), which is option (A).

Step-by-step explanation:

The student asks which ordered pair (x, y) satisfies both the linear equations 2x + 2y = 2 and 3x - y = 7. To find the solution, we can use substitution or elimination. Let's use elimination in this case:

• First, simplify the first equation by dividing by 2 to obtain x + y = 1.
• Next, multiply this new equation by 2 to get 2x + 2y = 2, which can be subtracted from the second given equation to eliminate y.
• Subtracting the equations, we get (3x - y) - (2x + 2y) = 7 - 2, simplifying to x - 3y = 5.
• This equation, combined with x + y = 1 from the first step, forms a system we can solve by substitution or elimination.

By solving the system we find that the correct ordered pair that satisfies both equations is (1, 0), so option (A) is the correct answer.