Caleb’s Blog

For this week’s blog post we will be taking a look at the 4 different ways of solving systems.

Our first way to solve is using graphs

The first step to solving a system with a graph is to get two slopes and of course have it on a graph

ex

The next thing to do is just look at our graph and just see where the two slopes cross through each other, and mark down the point where it goes through the points.

The next method is to use inspection

If we have two equations that are in simple form

ex:

x + y = 9

x – y = 1

we can just look at the equation, and inspect on what two numbers add to seven, and subtract to 1

in this case, the answer would be (5,4)

The next way to solve an equation is inspection, which mainly focuses on isolating a variable.

The first step is to have an x y equation

ex: 6x + y = 8  and 2x + y = 4

(note that this example is made to be an easy format to solve, and most equations will not be formatted this simple)

The first step, is to isolate a variable, and since we are given two equations where y does not have a coefficient, so we will isolate.

y= -6x + 8 and y= -2x + 4

since we have both variables isolated, and the statement is y=, we can an equation into y

for example y= -6x + 8 and y= -2x + 4 will now be turned into -6x + 8 = -2x + 4

Now what we need to do is to add like variables together, so we will move the x variables to the same side, as well as the constants to each side.

ex -6x + 2x = -8 + 4

now to add each variable together

-4x = -4

now to isolate x, we will divide -4 by -4

this will give us x=1

after this, plug x into the original equation, add like variables, and isolate y to get the final answer.

The last way to solve a system is elimination.

8x + y = 5

4x + 2y =10

first step is to make a zero pair, by multiplying a equation to make two numbers = 0

we will multiply 4x + 2y =10 by -2, because it will make a 0 pair with 8x + y = 5’s 8x

our equation now will be

8x + y = 5

-8x + -4y = -20

Now just add each like variable together

-3y = -15

now to isolate -3y just divide each side by -3 giving us

y = 5

now we would just go back to the original equation and plug 5 into y and solve for x to get our system point.

 

I chose this topic for my blog post, because I needed to review on the topic and display my understanding to myself.