Solve the system: x + y = 10 and x − y = 4

System of two equations in two unknowns. Elimination method (often easiest for ASVAB): add the equations to eliminate y. (x + y) + (x − y) = 10 + 4, giving 2x = 14, so x = 7. Substitute back: 7 + y = 10, so y = 3. Verify both: 7 + 3 = 10 ✓ and 7 − 3 = 4 ✓. Substitution method: solve first equation for y: y = 10 − x; substitute into second: x − (10 − x) = 4; simplify: 2x − 10 = 4; solve: x = 7; then y = 3. Both methods give the same answer. Elimination works well when adding or subtracting eliminates a variable (coefficients are opposites or equal); substitution works when one equation is easily solved for a variable. On multiple-choice tests, you can also test answers by substituting — efficient for systems.