Solve the system of linear equations by the elimination method.
D)The lines are parallel.
E)The lines coincide.

Question

Solve the system of linear equations by the elimination method. 
D)The lines are parallel. 
E)The lines coincide.

Quizplus · Accepted Answer

The given system of linear equations is:

2x - 3y = -7   ...(1)
4x - 6y = -14  ...(2)

We can eliminate the variable x by multiplying equation (1) by 2 and subtracting it from equation (2) as follows:

(2) - 2(1):
4x - 6y = -14
- (4x - 6y = -14)
-------------------
0x + 0y = 0

This implies that 0 = 0, which is always true.

Since we've obtained an identity, this system has infinitely many solutions. Specifically, any point on the line

y = (2/3)x + (7/3)

will satisfy both equations.

Solve the System of Linear Equations by the Elimination Method