Can anybody explain the systems of equations thouroghly and easily along with standard form and y intercept an

Question

big test coming up, can anyone break it down?

Answer 1

1. memorize the formulas

- standard form
- point-slope form
- slope intercept form

These are 3 ways to manipulate the same equation.

Memorization is the easiest way. If you have algebra basics down you can manipulate the equations from one form to the next. You won't need an explanation.

Answer 2

I disagree. Don't memorize, but understand.

Standard form of any equation means you have
(something) =0.
for a line it's ax+by+c=0, since a line is formed by an equation with x and y to the first power.
Note that ax+c=0 is a vertical line and by+c=0 is a horizontal line.

slope-intercept form is the equation solved for y. That is y=(something).
It so happens that it comes to y=mx+b.
m is the slope of the line. It's a ratio (even if the ratio is something:1). The numerator of the ratio is the "rise," or the amount y increases. The denominator of the ratio is the "run" or the amount x increases. So if you have y=(4/3)x + 8, for each increase of 3 in x, y will increase 4.
If you set x=0 in this equation, you will arrive at y=b. This gives you a point on the line (0,b). This is the point at which this line will intercept the y-axis.
note that lines of the sort x=a do not have a y-intercept because they are vertical lines and are parallel to the y axis.

Answer 3

You will need to be more specific on this one, this is a very broad question.

As for the test, I'm sure they won't ask you to explain what a system of equation is. In mathematics we don't work like that. You'll probably be given a system of equations and asked to solve it using various techniques. Now, there are many ways of solving the system of equations.

Say you are asked to solve the following system of equations simultaneously:

2x + 4y = 8
4x - 5y = 20

You can do it many ways (I am not sure which one you are familiar with).

The simpler and more easy to follow is;

Take 2x + 4y = 8 (make x the subject)

That is 2x = 8 - 4y
x = 4 - 2y (divide by 2)------------------(1)

Also take 4x + 5y = 20 (make x the subject)

That is 4x = 20 - 5y
x = 5 - 0.8y (divide by 4)-------------(2)

Since in (1) and in (2), the LHS is the same ( = x ), the RHS must also be the same. This means,

4 - 2y = 5 - 0.8y (make y the subject)
- 2y + 0.8y = 5 - 4
- 1.2y = 1
y = -1/1.2 = - 0.83333

Now either in (1) or (2), put the value for y to obtain the value for x

x = 4 - 2y
= 4 - 2(- 0.8333) = 5.6667

Thus y = - 0.8333 and x = 5.6667

Few things to note:

1. Signs ~ whenever an equal sign(=) is crossed the sign is changed. If it was positive, it is changed to negative and vice versa.
2. Your answers can be checked for correctness in any of the original equations given in the question. You simply put the obtained numerical values in the place of y and x respectively, and you will get the number in the RHS. In our case, you will get 8 if you substitute in the first ~ and get 20 if you substitute in the second.

Goodluck for your test!!