9.2 Systems of Linear Equations and Inequalities
Summative Worksheet #11: ANSWERS Check Homework PRE Objectives: To solve systems using substitution.
Lesson 9.2 Systems of Linear Equations & Inequalities Objectives: To solve systems using substitution. To solve systems using elimination. To put systems into triangular form so they can be solved with back substitution. For a system of linear equations in twovariables, exactly one of the following is true.
The system has exactly one solution. The system has no solution. The system has infinitely many solutions. Where the lines intersect 3 ways to kill a Vampire 1. Stake to the heart 2. Sunlight 3. Garlic unless your Edward & a Cross 3 ways to solve Linear Systems
1. By Graphing 2. By Substituting 3. Eliminating -1st make sure one equation has a variable isolated
In this case, one already is: x = -2y + 2 -2nd Substitute the expression into other equation Equation 1 x = -2y + 2 Equation 2 3 + y = 16 -2y + 2 x -3rdSubstitute answer into one of the equations 3( )+ y = 16 -6y y = 16 3x = 16 (-2) y -5y + 6 = 16 x = 6 -5y = 10 y = -2 ( , ) x 6 -2 y -1st make sure one equation has a variable isolated -2nd Substitute the expression into other equation -3rdSubstitute answer into one of the equations + -y =3 3x += -9 3x + y = -9 -1y = 3 y = -3 -3 3x -3 = -9 3x = -6 (-2,-3) x = -2 - -6y =-24 3x + 2y = 26 3x = 26 3x + 2y = 26 -6y =-24 ( ) y = 4 4 3x + 8 = 26 3x = 18 x = 6 (6, 4) Equation 1 3x 3y = 21 Equation 2 8x + 6y = -14 -Multiply Equation 1 by 2 8x + 6y = -14 Equation 1 (2)3x (2)3y = (2)21 6x 6y = 42 3x - 3y = 21 y = 21 + ( ) 14x + 0 =28 6 - 3y = 21 14x = 28 -3y = 15 x = 2 2 y = -5 (2, -5) Systems of Linear Equations
Here are two examples of systems of linear equations in three variables. System ofLinear Equations System inTriangular Form Ex 3. Use back-substitution to solve the triangular system.
-Start with the last equation & solve upwards. Ex 4. Use back-substitution to solve the triangular system.
-Start with the last equation & solve upwards. Classwork: Book: pg. 657; 6-10 all Classwork: Book: pg. 649; 7-25 odd