Emily R.

asked • 05/21/17

Solving Systems of Equations

Solve the system:
2x - 4y = 12
3x - 6y = 21

Kemal G.

Hi Emily,

You might have made a mistake when you typed the question. Because when I try substitution, it doesn't make sense. See below:
 
2x - 4y = 12
2x = 4y+12
x = 2y + 6
 
Now plug this in the other equation, i.e., 3x - 6y = 21
3(2y + 6) - 6y = 21
6y + 18 - 6y = 21
18 ≠ 21
 
Report

05/21/17

Arturo O.

In addition to the solution provided, note that the principal determinant of the system is
 
Δ = (2)(-6) - (3)(-14) = -12 - (-12) = 0 
 
which is sufficient to tell you there is no intersection of these 2 lines.
Report

05/21/17

1 Expert Answer

By:

Kenneth S. answered • 05/21/17

Tutor
4.8 (62)

Algebra II EXPERT will help you survive & prosper

See tutors like this
See tutors like this
Kemal has 'solved' the system, coming up with the inconsistency that 18 does not equal 21.
The work done so far is OK, but the PROPER CONCLUSION is that this is an inconsistent system, namely two non-intersecting lines.
 
A system of two inear equations in two unknowns may have
one point of intersection,
no points of intersection, or
infinitely many points, i.e. the two equations are different versions (multiples) of one equation--one entire line.
Upvote • 0 Downvote
More
Report

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.