Algebra 3 5.1/2 Systems of Linear Equations/Matrices

Intro o Remember that a system of equations, is a set of two or more equations containing one or more variables. o In general, you can solve a system that has no more variables than it has equations. o When you solve, you find a set of variables that fits each equation in the system.

o In the case of two linear equations, we can have: 1) One solution (lines intersect) 2) No solution (lines are parallel) 3) Infinitely many solutions (lines coincide)

Substitution 1) Choose a variable in one of the equations to isolate. 2) Substitute that result into the other equation. 3) Solve. 4) Substitute back into step 1.

Example 1 x – y = 5 x – y = 5 -3x +3y = 2

Elimination 1) Choose a variable to eliminate. 2) Multiply one or both equations by a constant, so that when added, the chosen variable is eliminated. 3) Solve for the remaining variable. 4) Substitute to find the other variable.

Example 2 3x – 2y = 0 5x + 10y = 4

Graphing o You can also choose to get each equation in slope intercept form, then graph to find the solution. o To get an accurate answer, use the intersect option on the calculator.

Matrices o We can rewrite a system of equations as an augmented matrix. o 3x +7y -8z =12 o 4x -9y =2

o Also matrices can be used in conjunction with the graphing calculator to easily solve complex systems.

Example 3 o Solve 2x + y -3z = 0 2x + y -3z = 0 -2x +2y +z = -7 3x -4y -3z = 7

Homework Page 516: 7-39 every other odd 41, 43, 45, 49, 51 41, 43, 45, 49, 51