SOLUTION: im having trouble understanding the systems of equations..... how do i solve by graphing?? for ex: y=x+2, y=-x+4?? i dont understand how to solve then graph it......!!!!

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: im having trouble understanding the systems of equations..... how do i solve by graphing?? for ex: y=x+2, y=-x+4?? i dont understand how to solve then graph it......!!!!      Log On


   

Question 114281: im having trouble understanding the systems of equations.....
how do i solve by graphing?? for ex: y=x+2, y=-x+4?? i dont understand how to solve then graph it......!!!!
Found 2 solutions by Fombitz, solver91311:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First you draw the two lines.
Where the lines intersect, the (x,y)point is a solution to the system of equations.
If the lines never intersect (that is, are parallel) then there is no solution.
+graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C+x%2B2%2C+4-x%29+
From the graph it looks like (1,3) is a solution to both equations.
Verify by substituting into each equation.
1.y=x%2B2
3=1%2B2
3=3
True statement
2.y=-x%2B4
3=-1%2B4
3=3
True statement
Your solution led to true statements from both equations.
Therefore it is a good solution.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
If you are asked to solve a system of linear equations by graphing, you just graph the two lines and the solution point is where the two lines intersect. Like this:



The red line is y=x%2B2 and the green line is y=-x%2B4 and we can see that they intersect at (1, 3). That means that x = 1 and y = 3 will make both of the equations true. Let's check that assertion:

3+=+1+%2B+2 is true, and
3+=+-1+%2B+4 is also true.

The method of solving a system of two linear equations in two varibles by graphing works quite well as long as the solution is nice neat whole numbers and the intersection of the two lines is right on top of the intersection of two grid lines. Other situations require other methods to get the exact answer, and you should be working on those other methods in your class the next few sessions.

Hope that helps.
John