Using elimination to solve a system:
*note you are trying to get zero pairs.
Step 1: to get a zero pair you need a negative and a positive number or variable. so with that said if you take a look at the example, what do you think is the easiest coefficient to multiply into any of these two equations to get a zero pair. remember there is more than one type of coefficient that can be multiplied into an equation to get a zero pair. I chose to multiply the second equation by -3.
Step 2: start solving for y by plugging in the x value into the first equation.
How to use substitution while solving a system.
*note we are trying to find the values of x and y.
Step 1: choose the equation with the with a simple variable, which is usually the one that has a coefficient of 1 in front of it. In this case since there is a 1 in front of both the y and x, you can choose whichever one you want. I am going to choose the y.
Step 2: we have to get the y by itself, so we have to move the 2x to the other side making it negative.
Step 3: plug in the y = -2x + 7 into the other equation and let algebra take over.
Step 4: once you have your answer, plug it into one of your equations. It doesn’t really matter which one you plug it into, but remember to work smart and choose which one is the easier choice. Once you have plugged it in, let algebra take over again and solve for y.
This week I learned the equation, slope y- intercept form. Which is this formula y=mx+b. Your main goal here is to isolate the y, below I have an example of how to get an equation into slope y. Which really means, to isolate the y.
Step 1: move #’s to the other side to isolate the y.
Step 2: use algebra to get the y by itself.
Step 3: solve to get your final answer.
This week I learned how to find the slope of parallel and perpendicular lines. What this means is that we can use the slope of a line to tell us whether two lines are parallel or perpendicular. Two lines are parallel if they have the same slope, and never cross. Two lines are perpendicular if the products of their slope is -1.
How to solve an equation using an output:
When solving an equation using an output you have to look at it backwards.
For example take a look at this equation.
You’re still trying to get x by itself and in order to do this you have to make a zero pair by adding 4 to each side. After you have done that you use BEDMAS which tells you to divide both sides by 7 which gives you x = 6.
How to find x and y intercepts in an equation:
Let’s say we have the following equation: y = 4x + 7
keep in mind that the x intercept – (x,0) y always = 0 and that the y intercept – (y,0) x always = 0.
Also remember that you’ll have to solve for x and y separately which will give you the coordinates for x and y on a graph.
Solving for x:
Solving for y:
How to use a table of values to show a relation:
An example would be: The cost of sour keys is related to the weight. The first step would be to figure out what the independent and dependent variables are. A good way to look at this is to think about which one depends on the other. Does the cost determine the weight of the sour keys, or does the weight of the sour keys determine the cost of the sour keys. I guess we can all say that when we buy sour keys at a store the amount (weight) of the sour keys always determines how much (cost) of the sour keys will be. The cost is the dependent variable and the weight is the independent variable, because the cost depends on the weight of the sour keys.
When we put this into a table this is how it will look:
Since we are finding out the cost of something we have to use some common sense, which in this case is that money can’t be negative numbers so we have to start at 0 and make our way up.
The equation for this relation would be:
The to figure out this equation would be to find out what the independent values which is the y column, goes up by.
This week I didn’t understand how to get the answer for the following question because I didn’t know the steps that had to be taken in order to solve this question. After asking for help I understood what to do to answer this question correctly. Below are the steps I took in order to solve this question.
Factoring simple trinomials when they have something in common: