This week, we have learned another method for solving linear systems. It is called elimination. The elimination method for solving systems of linear equations uses the addition property of equality. You can add the same value to each side of an equation. So if you have a system: x – 6 = −6 and x + y = 8, you can add x + y to the left side of the first equation and add 8 to the right side of the equation.
this week we have learned one of the method of solving a pair of a linear system, substitution. A linear system is defined as two linear equations line that will meet the same point on a graph. It also means that they both have the same x and y value. In order to find x and y, the easiest method is substitution.
for example, given a set of linear systems
2x-3y=-2 4x+y=24
1. we will first need to isolate y at one side, makes the equation as “y=-4+24”.
2. after that we have to sub the “y=-4+24” into 2x-3y=-2, therefore will becomes 2x-3(-4+24)=-2, we calculate this equation and found out that x=5.
3. now sub back the x=5 into 4x+y=24 and we will get y=4
Then the solution of the points x,y will be (5,4).
But are still some steps and hints(conclusion)that I learned from Ms. Burton’s class:
This week we have learned the last type of linear function called general form, which is Ax+By+C=0. General form can be formed by slope-intercept and point-slope form. The following are the examples of converting both linear equations to general form.
Last week, the formula linear equation has been introduced to us. A linear equation refers to the equation of a straight line. There is a formula y=mx+b. m is equal to the slope and b is the y-axis. If there is a given graph and require us to find write out the equation, it’s easy by using the formula.
For example, in this graph, we can found out the slope by finding two points (0,1) (1,3) and using the slope formula the slope will be 2 and we can find out the b by looking at the point which the straight line and the y-intercept crossed together which is 1. The complete formula will be y=2x=1.
This week, we continued the chapter, Functions. And we go in deeper for this chapter, to calculate functions, as we have known that the x is the input and the y is the output. When we see a question like f(x)=2x+3. The f refers to the name of the function. the (x) is the input x the output y is 2x+3. Usually, x will be given as a number in order to calculate y . for example f(5)=2x+3. in this case, it means x=5 then, we have the sub the number 5 into 2(5)+3. then we can get the output. But in other cases, we will be given a graph to find out.
y.
This week we have learned about functions, to identity functions, there’s some rules. First, the input x cannot be the same, they all should be different in order to get different outcomes, one input x cannot be resulted to many output, it can only resulted to one output y. but sometimes the output y will be resulted from numbers of input x. Here’s is an example:
Moreover, the vertical line test can be used to determine whether a graph represents a function. A vertical line includes all points with a particular x value. The y value of a point where a vertical line intersects a graph represents an output for that input x value. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that x value has more than one output. A function has only one output value for each input value.
This week we have learned about domain and range which takes an important role in this topic. when looking at a graph, the domain represents the x-coordinates which is the independent value, while the range represents the y-coordinates which is the dependent value.
There are usually two types of graph to show the relation, one type is using dots, while one is using a line or a curve. But they have differences. Graphs that are composed of a series of dots are referred to as discrete graphs. A discrete domain is a set of input values that consist of only certain numbers in an interval because dots between dots are separate and are not connected, so they don’t have any linkage.
Another type of graph are composed of a connected curve are referred to as continuous graphs. A continuous domain is a set of input values that consists of all numbers in an interval, which means values can be decimal or fractions.
This week is the first time to write blog post after Easter break. As the virus is getting worse, students are asked to stay at home and continue our education by online learning using teams, which takes both teachers and students some time to explore it and planning our schedule again. But starting from last week, all things are well fixed and planned.
We have learned a method to factor “ugly” trinomials (ones that have a leading coefficient that does not factor out as a GCF), which is different from the “difference of perfect squares” and “greatest common factor” method. the following is an example.
first, let 6*(-40)=-24 . next we are going to list out the factors of -24 and find a pair of factors that have the answer -23 when doing plus or minus. After that write the two numbers into the square and then we are able to find out the answer.
This week we have learned about factoring meaning changing a simplified polynomial into the primeval form, which means it had not done any expanding or simplified. To do this, there is some easy method and rules. First, the whole Polynomial should be positive, it cannot be factorized if it is a whole negative question. It also can’t be factorized if the constant term is negative. I have written an example below to explain it.
This week we have learned the different methods of solving polynomials the following are the two methods that o often apply when I solving polynomials.
1st method: distribute method
For this method, the first thing we need to do is to distribute each term of the first polynomial to every term of the second polynomial. then combine the terms(add or subtraction) and simply the answer.
2nd method: algebra tiles method
algebra tiles are square and rectangle-shaped tiles that represent numbers and variables.
