Unit+7

Unit 7 In this unit we begin to explore solving systems of equations, which are two or more equations with two or more variables solved simultaneously.



There are 4 methods for solving systems of equations: 1. Graphing 2. Substitution 3. Elimination 4. Combination (mostly used with elimination/substitution)

The first method we explored was graphing and we reviewed how to graph linear equations in both slope-intercept and standard forms. In Slope-intercept form, the equation is written in such a way that the coefficient of x is the slope, and the constant is the y-intercept.

In order to solve a system of equations by graphing we need to know how to graph a linear equation. If you forget how to graph a linear equation, you can watch this video as a refresher. The teacher moves very slowly and explains things well.

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Once you look at the video or review my notes on graphing linear equations in slope-intercept form, try working on this worksheet for practice You must graph both equations on the same coordinate plane and be able to identify their intersection. The coordinates of their intersection represent the values of the two variables for which you are solving.

Take a look at my notes for Section 7-1 to see a few examples of solving a system by graphing

If you would like more practice solving systems of equations using graphing you can work on this page. The answers follow the problems. I sort of combined sections 7-1 and 7-4 together so I'm including those notes and practice here as well. 7.4 was an exploration on Consistent and Inconsistent Systems. Remember that if the system has one or an infinite number of solutions then the system is considered Consistent. One solution=consistent independent. Infinite solutions=consistent dependent. If the equations form parallel lines or there is no solution then the system is considered Inconsistent. Here are the notes if you are still confused.

In Section 7-2 we talked about the second way to solve a system of equations- that is, to use the Substitution Method. In this method we must first make sure that one of the equations in the system is solved for one of the variable. The you substitute the equivalent expression into the other equation and solve.

This is what a problem would look like:



Here are the notes on that section. After you've taken some notes and think you understand them, try doing this worksheet.

Lastly, we examined the third approach to solving a system of equations. That was the Elimination Method. In this method we eliminated one of the variable by combining opposite terms. Sometimes the system had opposite terms in the beginning, sometimes we had to create opposite terms by multiplying one or both of the equations by something. We practiced this method with a worksheet. Here are the notes from that section.

Here is a lot of practice problems to review.

In section 7-5 we left equations and talked about how to solve systems of inequalities. Remember that there is no one solution to a system of inequalities, but numerous answers. We solve a system of inequalities by graphing and finding an overlapping shaded region of both inequalities. Remember two things: 1. Do we use a solid or dotted line? 2. Do we shade above or below the line?



Do you want practice with solving inequalities, try this worksheet.

The last thing we did in Unit 7 was talk about some application of systems of equations by exploring some classic two-variable word problems. We discussed 5 types: 1. Digit Problems 2. Coin Problems 3. Age Puzzles 4. Speed/Wind Problems 5. Chemical Solution Problems

Here are the notes for that section. Have fun trying some of these fun problems. If you need more practice here is another worksheet.