Predict the result
Solve the system y equals negative one half x minus one, and y equals two x minus eleven.

Set up the model
At a common point, both y expressions are equal.
Equate them and solve for x, then substitute for y.

Work the example
The equation gives x equals four.
Substitution in both original equations gives y equals negative three.

Check the result
Compare y equals two thirds x minus five with negative four x plus six y equals zero.
Take eight seconds to think before the answer appears.
[Eight-second silent pause to work; the answer remains hidden.]
The slopes are equal but the intercepts differ, so the distinct parallel lines have no solution.

Interpret the result
A system solution must satisfy both original equations at the same point.