Review of Chapter 8: Solving A System of Linear Equations

From class, we had the problem: 3x + (1/3)y = 10; 2x - (5/3)y = 35. So, multiply 3 to everything. So, 3(3x + (1/3)y = 10); 3(2x - (5/3)y = 35). Therefore, you have 9x + y = 30; 6x - 5y = 105, respectively. Now, multiply the first linear equation by 5:5(9x + 5 = 30). So, 45x + 5y = 150; 6x - 5y = 105. Add them, and you get, 51x = 255. Therefore, x = 5. Using the second equation, plug in 5 for x. So, 3(5)+(1/3)y = 10. Therefore, 15 + (1/3)y = 10. Solve for y. So, (1/3)y = -5. Then, multiply each side by 3. So y = -15. QED

Carbon Dating - Exponential Relationship

AI tried to show a Star Trek clip, but couldn't get it. So here is a clip from Numb3rs about carbon dating.

Solving a Three Variable System of Equations

Here is the problem from class: a + b + c = 5, 2a + 3b + c = 10, 4a - b + c = 9. So, solve for c in the first equation. c = 5 - a - b. So, substitute the equation of c into the other equations. 2a + 3b + 5 - a - b = 10, 4a - b + 5 - a - b = 9. So, simplify the equations. a + 2b = 5, 3a - 2b = 4. So through elimination, add the equations. 4a = 9, therefore a = 2.5. So let's use two equations: a + b + c = 5, 4a - b + c = 9. So through elimination, add the equations. 5a + 2c = 14, and since a = 2.5, 5(2.5) + 2c = 14, 12.5 + 2c = 14, 2c = 1.5 and therefore, c = .75. So, a + b + c = 5 with the values of a and c, look like: 2.5 + b + .75 = 5. Solve for b. b = 1.75. Check your work and the values add up to 5.

Hey, 8th Graders...Solving Linear Equations by Graphing

The first video helps you set up the problem. The next video helps you solve for y. To find the intersection point, we have been using the graphing calculator. Remember that y min and x min is zero. The y max and x max is higher than the highest y-intercept in your problem.

Honors Algebra: Solving An Equation by Grouping

Hi, everyone. I found this video on YOUTUBE!

Honors Algebra Extra Credit is due April 8, 2013

Remember that: Area of a circle is (pi)x(radius)squared; Area of a rectangle is (length)x(width); Area of a triangle is .5(base)x(height); Perimeter of a rectangle is 2(length) + 2(width) Watch the video on solving a geometry problem. Do pg.585 #49-51. Copy the pictures, show your work, answer the problem. Now after completing that, solve this next problem. You have a rectangular yard whose area is x squared plus 32x plus 231. What are the dimensions of the rectangular yard? What if you knew that x equaled 10, what are the dimensions of the yard and the area of the yard? Turn in all of your work, neatly, on April 8, 2013.

8th Grade Extra Credit is due April 8, 2013

1. Find a relative that has a cell phone. Ask them about the initial cost of the cell phone and the charge per minute. Create an equation based on the information calling it C, in the form: C = mx + b. Find a different relative that has a cell phone. Ask them about their initial cost of the cell phone and the charge per minute. Create a second equation based on the information calling it C'', in the form: C'' = mx + b. 2. Watch the video below. 3. Just as we did in class, set the two equations equal to each other, find the value of x (in minutes). 4. Now, take that value of x and plug it into C or C'' to get the cost. 5. Create a graph and graph the two equations similar to Mr. Taylor's sample problem. Watch the video below for an idea of what to do.