Solve 3x - 2y = 10 and x + 3y = 7 simultaneously

Analyze the question: We have two linear equations in two unknowns. We need the pair (x, y) that satisfies both.

Concept: Simultaneous equations can be solved by elimination or substitution. Here, substitution works nicely because the second equation has x with coefficient 1.

Solution:

Equation (1): 3x − 2y = 10 Equation (2): x + 3y = 7

From (2): x = 7 − 3y

Substitute into (1): 3(7 − 3y) − 2y = 10 21 − 9y − 2y = 10 21 − 11y = 10 −11y = −11 y = 1

Then x = 7 − 3(1) = 4

Check:

• Equation (1): 3(4) − 2(1) = 12 − 2 = 10 ✓
• Equation (2): 4 + 3(1) = 7 ✓

So x = 4 and y = 1, which matches option D.

Tip: In multiple-choice simultaneous equations, you can save time by plugging the options into the equations. Option A (x = −4, y = 1) fails immediately in equation (2): −4 + 3 = −1, not 7. Always check the simpler equation first to eliminate wrong options quickly.