SOLUTION: Solve the system of equations by graphing x-y=2 x+y=6

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve the system of equations by graphing x-y=2 x+y=6       Log On


   

Question 198374: Solve the system of equations by graphing
x-y=2
x+y=6
Found 2 solutions by arallie, jim_thompson5910:
Answer by arallie(162) About Me  (Show Source):
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:


system%28x-y=2%2Cx%2By=6%29


In order to graph these equations, we must solve for y first.


Let's graph the first equation:


x-y=2 Start with the first equation.


-y=2-x Subtract x from both sides.


y=%282-x%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=x-2 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=x-2.


-------------------------------------------------------------------


Now let's graph the second equation:


x%2By=6 Start with the second equation.


y=6-x Subtract x from both sides.


y=-x%2B6 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=-x%2B6.


-------------------------------------------------------------------


Now let's graph the two equations together:


Graph of y=x-2 (red). Graph of y=-x%2B6 (green)


From the graph, we can see that the two lines intersect at the point . So the solution to the system of equations is . This tells us that the system of equations is consistent and independent.