To find x and y, we solve the system of linear equations using elimination or substitution. Solving 3x + 2y = 26 and 2x + 3y = 19 gives x = 8 and y = 1. Their difference x − y is therefore 8 − 1 = 7, a clean integer result consistent with both equations.
Option A:
Option A, 5, would be the difference if the values of x and y were closer together, but solving the system shows a larger gap between them. It does not match the algebraic relationships specified.
Option B:
Option B, 6, again does not arise from any correct elimination or substitution procedure. When checked against the solved values of x and y, it fails to match their actual difference.
Option C:
Option C reflects the correct outcome after systematically eliminating one variable and solving for the other. Substituting back gives consistent values of x and y whose difference is exactly 7, agreeing with all the given equations.
Option D:
Option D, 8, overshoots the true difference and would imply values of x and y that do not satisfy both equations simultaneously.
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