Solving Systems of Equations by Graphing | MathHelp.com - By MathHelp.com
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| 00:0-1 | To solve for two separate variables . In this case | |
| 00:04 | X&Y . We need to separate equations called a system | |
| 00:10 | of equations . There are different ways of solving systems | |
| 00:15 | of equations . But in this section we're going to | |
| 00:18 | be using the graphing method to solve the system of | |
| 00:23 | equations by graphing , we would first graph each of | |
| 00:28 | the two given lines and what we're looking for is | |
| 00:32 | their point of intersection . This point where the two | |
| 00:37 | lines intersect will represent the X and Y . That | |
| 00:43 | is the solution to this system of equations . So | |
| 00:48 | let's start by graphing the line Y equals three halves | |
| 00:52 | , X plus one . It has a Y intercept | |
| 00:56 | of one And its slope is 3/2 . So we | |
| 01:02 | go up three and over two . And we have | |
| 01:09 | our first line for our second line , Y equals | |
| 01:14 | negative X plus six . It has a Y intercept | |
| 01:18 | of six up six units on the y axis and | |
| 01:24 | its slope can be thought of as negative one or | |
| 01:28 | negative 1/1 . So from our y intercept we go | |
| 01:32 | down one and to the right one to plot a | |
| 01:36 | second point notice that if we go down one and | |
| 01:41 | to the right one again we reach our point of | |
| 01:45 | intersection . So if we graph are second line , | |
| 01:50 | you can see that the two lines intersect at this | |
| 01:54 | point which has the coordinates to four . Yeah right | |
| 02:04 | . In other words when X equals two and Y | |
| 02:09 | equals four , we have the solution for our system | |
| 02:14 | of equations . It's very easy to check your answer | |
| 02:18 | by plugging these values for X and Y back into | |
| 02:22 | each of the two original equations to see if they | |
| 02:26 | work for our first equation , Why is four equals | |
| 02:36 | three halves times X , which is to plus one | |
| 02:45 | , the two's cancel , we have four equals three | |
| 02:47 | plus one , So four equals 4 . and our | |
| 02:52 | first equation checks for our second equation , why is | |
| 03:00 | four equals negative X , which is negative two plus | |
| 03:10 | six , So four equals 4 . And our second | |
| 03:15 | equation checks , so the solution to this system of | |
| 03:20 | equations must be the point 24 |
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