Quarter 3 Pba

Colin Woodward's quarter 3 pba

• Hello, this presentation will cover the main ideas and focus points in the 3.5 unit of Algebra 2.

Algebra 2 unit 3.5

• In Unit 3.5, the main focus is to solve 2 variable equations.
• There are 2 simple ways to do this.

Unit 3.5 terms

• Before we get started, you must know some basic terms...
• Solution: any ordered pair of numbers that is a solution of each equation in the system

Unit 3.5 terms

• Equivalent Systems: systems that have the same solution set
• Consistent System: a system that has at least one solution (equations that will intersect)

Unit 3.5 terms

• Inconsistent System: a system that has no solution (equations that are parallel, slopes are equal)
• System of Linear Equations: a set of linear equations in the same 2 variables

Algebra 2 unit 3.5

• As was said earlier, there are 2 simple methods for solving a 2 variable equation.:
• Substitution and Linear Combination

Substitution

• In substitution, you must solve one of the equations for a variable.
• Originally, it will look something like: y+2x = 5, and after the first step, it should look like: y = -2x+5.
• Then, insert the Y value to the next equation which might look like: y+3x = 10.

Substitution

• After solving for Y, you must plug in the value for Y (the equation we just solved) into the other equation to solve for X.
• The other equation could look like: y+3x = 10.
• After plugging in the equation for Y, it should look like: (-2x+5)+3x = 10.

Substitution

• Solve the equation for X according to the order of operations, and the solved equation should look like: x = 5.
• After we have solved for X, we can go back and solve for Y using either equation, this should look like: y+2(5) = 5.

Substitution

• After we have solved for X, we can now solve for Y using either equation. This should look like: y+2(5) = 5. After solving correctly, the solved equation for Y should look like: y = -5.
• We should then group the X and Y values together which should look like: (5, -5).

Substitution

• Here is another example, found from www.khanacademy.org.

Untitled Slide

Linear combination

• In linear combination, you will either add or subtract the equations, depending on the set values for the problem.
• For example, if you were solving a problem with x-y = 1 and x+y = 1, you would add to eliminate the Y's to get 2x = 2.

Linear combination

• To begin walking this through step by step, we can begin with a problem of x+y = 5 and x-y = 13.
• We can start by adding the 2 equations, the difference should look like this: 2x = 18.

Linear combination

• After determining that 2x = 18, we can also see that x = 9, which will go into our next equation to solve for Y.
• Now we can replace X in either one of the original equations (I used the first equation), which should look like: (9)+y = 5.

Linear combination

• After solving for Y according to the order of operations, we can determine that y = -4.
• Lastly, we can put our answers inside parentheses to show where the 2 lines will intersect, which should look like: (9, -4).

linear combination

• Here is another example from www.khanacademy.com.
• The solution was attempted with linear combination, but substitution worked better.

Untitled Slide

Review

• To review, let's go over some more example problems for you to try on your own.
• You may use any method you would like.

Review

• First Problem: x+y = 9 and x-y = 13

Review

• If you got (11, -2), you are correct!
• Second Problem: 2x+3y = 12 and x+y = 3

Review

• The answer to that question is (9, -6).

Review

• Congratulations! You now know how to solve 2 variable equations with 2 equations.
• Good Job!