Algebra 2 - Systems of Linear Equations + Inequalities

Unit 1: Systems of Linear
Equations and Inequalities
Algebra 2 Honors

,1.02: Solve Systems of Two Linear
Equations

,Linear Equations

- standard Form:
- Ax + By = C
- slope-Intercept Form
- y = mx + b
- point-Slope Form
- y-y1= m(x-x1 )

, System of Equations

- two or more equations to be solved together
- the solution must satisfy all the equations in the system
- there are three types of systems of equations:
- linear system with “unique” or “one” solution
- consistent and independent
- the lines will intersect at one point when graphed
- linear system with “no” solution
- inconsistent
- the lines will be parallel when graphed and will never touch
- linear system with “infinitely many” solutions
- consistent and dependent
- the lines will follow the same path when graphed and essentially be the
same line
- when solving for a linear system with one solution:
- when graphed, the point that the lines intersect at is the solution
- the solution will always be an ordered pair
- when a system of equations solved algebraically results in an
equation that is true for all real numbers, the system has
infinitely many solutions. when it results in an equation that is
not true for any real numbers, the system has no solution.