Math 10 Week 17- Systems of Linear Equations

This week we started our last unit on Systems of Linear equations. We have covered all the new information needed for grade 10 math.

We learned about the process of substitution and elimination to solve the x and y coordinates. Substitution is an algebraic method of finding solutions. Eliminations is used when all variables doesn’t have a coefficient of 1.

Substitution example:

First, make sure you are able to use the substitution method by checking if the coefficient of a variable is 1, and isolate that variable. Take the answer of the isolated variable and plug it into the other equation, this will make the equation contain only one variable(either x or y). Group the numbers and variables together and work out the equation until you can isolate the variable. Once the variable is isolated all you have to do is take the number and plug it into the first equation you were working with to get the other variable.

Elimination example:

Usually the elimination method is used when the variables doesn’t have a coefficient of 1. First, change the equations into standard form to make it easier to look at, and choose one pair of variables to make zero pairs. Add the two equations together and isolate the variable. Plug in the answer of the isolated variable into one of the original equations, and solve the equation until you are able to isolate the other variable.

Math 10 Week 16- Linear Equations of Lines

This week we learned about the different equations to make the equations of the line.

The most important thing to find is the slope(rise/run). Which we can figure out with 2 clues(x,y).

Slope y- intercept form: y=mx+b

Point- slope form: m(x-x)=y-y

General form(pretty form): ax+by+c=0

-A >0

-A,B,C all have to be integers.

– To get to general form you first have to get it to slope y intercept form or point slope form.

 

Math 10 Week 15

On the 15th week we learned more about slopes.

Colinear: points lining up

Parallel lines: lines that never cross and have the same slope. Ex) m1= m2

Perpendicular lines: two lines that meet at 90 degrees. Ex) m1= 3/4, m2= -4/3

We also started to learn about how to incorporate the last unit domain and range to this unit.

 

Ex) In a linear equation the amount that y1 to y2 increases or decreases by would be the slope(6) multiplied x. When you multiply the slope(6) to the input(1) you should get the output(2). If it isn’t equivalent then the number that would be added or taken away to get the output, which in this case -4 would be the y-intercept.

Math 10 Week 14- Slope of a Line

This week in math we started a new unit on slopes.

We learned that a slope is a number that describes the steepness of a line, which is the same as the tangent ratio(trigonometry).

slope= rise(y)/ run(x)

Positive slope: The slope rises from left to right

Negative Slope: The slope decreases from left to right

 

 

 

Math 10 Week 13- Domain and Range

This week in math we learned more about relations and functions. We reviewed how to write out inequalities and we also learned about domain and range. At first I was confused about the whole concept of the input and outputs but once I got used to solving more equations it got easier to do.

Domain: the independent(input) variable in the relation.

Range: the set of all numbers for the dependent(output) variable in the relation.

Function: a special realtion where every input(x) has only one output(y).

Function Notation:

To evaluate a function you would have to substitute the variable with the given number which in this case would be 5 and -8. To solve the equation remember to always use B.E.D.M.A.S!!

Math 10 Week 12

This week in math we started to learn about relations and functions. We reviewed linear relations from grade 9. And we learned how to find the intercepts of x and y on a graph.

To find the the x intercept you would multiply the y to 0. Then you would single out the x by deviding both sides by 4.

To find the y intercept you would multiply x by 0, and devide both sides by 7 to single out the y.

With the two answers you are now ready to draw the graph.

Math 10 Week 11- Mid term review

On week 11 of math we reviewed all the units for our mid terms. One thing I forgot and had to review was how to catagorize numbers into groups from chapter 1.

R stands for real numbers which are all numbers including rational and irration numbers.

The Q with the line on too of it stands for irrational numbers which are also known as “ugly numbers”. They are numbers that cannot be written as a fraction.

Q stands for rational numbers. They are all the numbers that can be written as a fraction.

I stands for integers. They are all positive(whole) numbers including negative numbers.

W stands for whole numbers. Which are all positive natural numbers including 0.

N stands for natural numbers. They are all the positive numbers.

 

Math 10 Week #10- Factoring Trinomials

This week of math we learned how to factor trinomials.

Example 2) Find the possible 2 integers that equal to 24 when multiplied together. Pick the pair of integers that equal to 11 when added together. Make sure to see if the integers have to be possitive or negative depending on the middle and last number (11, 24). If there is no pair that equals to the middle number when added together, it can’t be factored. The integers can be written in any

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