Substitution, Elimination, Graphing, Matrices Solving Systems Substitution, Elimination, Graphing, Matrices Day 1 Substitution: Solve 1 equation for 1 of the variables Substitute the solved variable in the 2nd equation Distribute/CLT to find variable 1 Substitute the found value back in to 1 equation to find the 2nd variable

Day 2 Elimination: Multiply 1 or 2 equations by some #’s to attain opposite coefficients of at least 1 of the variables Add the 2 equations together Repeat process with Substitute the found value back in to 1 equation to find the 2nd variable

Day 3: 3 Variable systems by hand Use the elimination process on two of the original equations to eliminate one variable. Creates equation 4 Take third equation and one of the others and use elimination to eliminate same variable as before. Creates equation 5 Use elimination with equations 4 and 5 to get down to one variable. Substitute that value into equation 4 or 5. Solve for remaining variable. Substitute both values into one of original 3 equations to solve for final variable.

Day 4 Matrices: Get your calculator! Hit 2ND, 𝑥 −1 , for MATRIX→→EDIT, ENTER Type in the matrix size, REMEMBER ROWS BY COLUMNS Type in the coefficients for the first equation, then second, then third… Go to your home screen at hit 2ND, 𝑥 −1 , for MATRIX→MATH and look for rref( Hit ENTER then 2ND, 𝑥 −1 , for MATRIX and select the matrix

Partial Fraction Decomposition Factor denominators and separate into the partial fractions The number of factors and multiplicity determines the number of fractions The degree of each factor determines the look of the numerator (numerator is a degree less than denominator) Multiply by the LCD Distribute and rearrange Solve the system