Question

Solve the system of equations using the elimination method. Show your steps.1/3x+y=3,2y=−2/3x+10

Answer 1

Write the system as
(1) (1/3)x + y = 3
(2) 2y = −(2/3)x + 10.

Clear fractions by rewriting (2) and multiplying both equations by 3:

From (2): (2/3)x + 2y = 10.
Multiply (1) by 3: x + 3y = 9.
Multiply the rewritten (2) by 3: 2x + 6y = 30.

Now eliminate by using 2·(x + 3y = 9) = 2x + 6y = 18. Subtracting this from 2x + 6y = 30 gives

0 = 12,

a contradiction. Therefore the system is inconsistent and has no solution (the two lines are parallel: y = −(1/3)x + 3 and y = −(1/3)x + 5).