Question

What is the solution of this system of linear equations?

3y = 3 y equals StartFraction 3 over 2 EndFraction x plus 6.x + 6

y – StartFraction one-half EndFraction y minus StartFraction 1 over 4 EndFraction x equals 3.x = 3

(3, 6)
(2, 1)
no solution
infinite number of solutions

Answer 1

Interpret the system as
1) 3y = (3/2)x + 6
2) y − (1/2)y − (1/4)x = 3

Simplify each:
1) y = (1/2)x + 2
2) (1/2)y − (1/4)x = 3

Substitute y from (1) into (2):
(1/2)((1/2)x + 2) − (1/4)x = 3
(1/4)x + 1 − (1/4)x = 3
1 = 3, a contradiction.

Therefore the system is inconsistent and has no solution.