Page 34 - Algebra

When it comes to the system of linear equations,
• The lines may intersect at a single point; the pair of equations will have a unique solution. Such equations are called a consistent pair of equations.
• The lines may be parallel; the pair of equations will have no solution. Such equations are called inconsistent pair of equations.
• The lines may be coincident; the pair of equations will have infinitely many solutions. And, such equations are called dependent pair of equations.
Worked Example
Find whether the pair of equations has no solution, a unique solution, or infinitely many solutions.
3x – 4y = 5
4x + 5y = 12
Solution:
Plot the equation on the graph.
Point of intersection
The equation intersects at one point.
So, the equation has a unique solution.
For a system of linear equation
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
You can compare the ratios of two equations algebraically by comparing the ratios of the coefficients.
Page 33 of 177
Algebra I & II