MA129 Lecture 10: Linear Algebra
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Document Summary
Solution set of a linear system: set of points that satisfy both equations. Consistent system: there is one solution or more. A system of linear equations (linear lines) can have: no solution (two parallel lines, unique solution (one intersection point) Note: one line is a scalar (k) multiple of the other line. Example: solve the system: x + 2 = 4 y and x. Label the equations (1) and (2) then isolate one variable in one of the equations and substitute that variable into the other equation. 3 2 + y = 3 y) x = 4 2 y y (1) (2) (4. 1 6 + y = 3 y. 3 = y into one of the equations. y and let y = 3. Then find x by substituting y x = 4 2 (3) (1) x = 4 2 x = 4 6. Therefore, there is only one solution: x, ) ( y = ( 2 3.
