Today we covered Section 7.3 and 7.4 from the book, about solving a linear system y linear combination, and the applications of linear systems.<\/p>\n
To step a linear system by combinations, follow the following 4 steps:<\/p>\n
1. Arrange the equations with like terms in columns;<\/p>\n
2. Multiply one or both of the equations by a number to obtain coefficients that are opposites to one of the variables;<\/p>\n
3. Add the equations from Step 2. Combining like terms will eliminate one variable. Solve the remaining variable;<\/p>\n
4. Substitute the value obtained from Step 3 into either of the original equations and solve for the other variable;<\/p>\n
5. Check the solution in each of the orginal equations.<\/p>\n
We did some classroom exercises together. Thanks go to those students who volunteered. As I told them, don’t be afraid to make mistakes and it is totally OK to make mistake.<\/p>\n
We talked about the importance of the last step, to check, as this is the step where you can find out if you have made any mistake, and get a chance to fix the mistake.<\/p>\n
For the word problems, we talked about three steps to come up with the equations:<\/p>\n
1. Have a verbal model by drawing squares with words in them;<\/p>\n
2. Pick variables x and y to represent some values;<\/p>\n
3. Come up with the algebraic model which contains two equations.<\/p>\n
Then use any approach to solve the equations.<\/p>\n
For homework, find it below:<\/p>\n