Question

Solve the system of equations {2x + 3y = -5 by the BEST method. Explain your choice.
{7x - 3y = 23

Answer 1

Best method: elimination — the y-coefficients are 3 and −3, so adding the equations eliminates y immediately.

Add the two equations:
(2x + 3y) + (7x − 3y) = −5 + 23
9x = 18 ⇒ x = 2.

Substitute x = 2 into 2x + 3y = −5:
4 + 3y = −5 ⇒ 3y = −9 ⇒ y = −3.

Solution: (x, y) = (2, −3).

Check: 7(2) − 3(−3) = 14 + 9 = 23, and 2(2) + 3(−3) = 4 − 9 = −5.