Solve the equation; 3x - 2y = 7, x + 2y = -3

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

3x - 2y = 7 ... (i) x + 2y = -3 ... (ii)

Concept: Use the elimination method. The y-terms (-2y and +2y) are opposites, so adding the equations removes y.

Solution:

Add (i) and (ii):

3x + x - 2y + 2y = 7 + (-3) 4x = 4 x = 1

Substitute x = 1 into (ii):

1 + 2y = -3 2y = -4 y = -2

Check in both equations:

• (i) 3(1) - 2(-2) = 3 + 4 = 7 ✓
• (ii) 1 + 2(-2) = 1 - 4 = -3 ✓

Check the other options quickly:

• B (1, 3): 1 + 6 = 7 ✓ in (i), but in (ii) 1 + 6 = 7 ≠ -3 ✗
• C (-2, -1): in (i) -6 + 2 = -4 ≠ 7 ✗
• D (4, -3): in (i) 12 + 6 = 18 ≠ 7 ✗

Answer: x = 1, y = -2, which is option A.

Tip: When the coefficients of one variable are equal and opposite, just add the equations. Always substitute your answer back into both equations. In multiple choice, you can also test the options in the equations to save time.