SOLUTION: x+y=7 x-y=1 Solve the system of equations by graphing. Then classify the system. Use the graphing tool to graph the system. If both equations yield the same line, graph the

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: x+y=7 x-y=1 Solve the system of equations by graphing. Then classify the system. Use the graphing tool to graph the system. If both equations yield the same line, graph the      Log On


   

Question 198271: x+y=7
x-y=1
Solve the system of equations by graphing. Then classify the system.
Use the graphing tool to graph the system. If both equations yield the same line, graph the line twice.
Found 2 solutions by arallie, jim_thompson5910:
Answer by arallie(162) About Me  (Show Source):
You can put this solution on YOUR website!
+graph%28+300%2C+200%2C+-10%2C+10%2C+-10%2C+10%2C+7-x%2C+x-1%29+
x%2By=7 and x-y=1
Add
x%2By=7
x-y=1
2x%2B0y=8
Simplify
x=4
Substitute
%284%29%2By=7
Solve
y=3
Check
%284%29-%283%29=1
1=1Check

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%2By=7%2Cx-y=1%29


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


Let's graph the first equation:


x%2By=7 Start with the first equation.


y=7-x Subtract x from both sides.


y=-x%2B7 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=-x%2B7.


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Now let's graph the second equation:


x-y=1 Start with the second equation.


-y=1-x Subtract x from both sides.


y=%281-x%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=x-1 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=x-1.


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Now let's graph the two equations together:


Graph of y=-x%2B7 (red). Graph of y=x-1 (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.