Solving Linear – Quadratic Systems
A pair of linear equations, considered together, is called a linear system. To solve a linear system with two
variables such as x and y means to find all the ordered pairs (x, y), if any, that satisfy both equations. These may
be found by graphing both equations on the same axes.
Intersecting Lines Parallel Lines Coincidental Lines
(a, b)
(a, b) is the only solution There is no solution There are infinitely
and there is one solution many solutions
Example: Solve graphically
a) 2x + 3y − 12 = 0
3x − 2y − 5 = 0
A pair of linear equations, considered together, is called a linear system. To solve a linear system with two
variables such as x and y means to find all the ordered pairs (x, y), if any, that satisfy both equations. These may
be found by graphing both equations on the same axes.
Intersecting Lines Parallel Lines Coincidental Lines
(a, b)
(a, b) is the only solution There is no solution There are infinitely
and there is one solution many solutions
Example: Solve graphically
a) 2x + 3y − 12 = 0
3x − 2y − 5 = 0
