SOLUTION: Graph the linear system and estimate the solution. Then check the solution algebraically. x+2y=9 -x+6y=-1 thanks in advance

Algebra ->  College  -> Linear Algebra -> SOLUTION: Graph the linear system and estimate the solution. Then check the solution algebraically. x+2y=9 -x+6y=-1 thanks in advance      Log On


   



Question 164302: Graph the linear system and estimate the solution. Then check the solution algebraically.
x+2y=9
-x+6y=-1


thanks in advance

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Transform both to slope-intercept form and graph.
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x%2B2y=9
2y=9-x
y=%289-x%29%2F2
Slope = -1/2, Y-intercept=9/2
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-x%2B6y=-1
6y=x-1
y=%28x-1%29%2F6
Slope=1/6, Y-intercept=-1/6
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Then graph the two lines.

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Looks like (7,1) is the solution.
Check using the equations.
x%2B2y=9
7%2B2%281%29=9
7%2B2=9
9=9
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-x%2B6y=-1
-7%2B6%281%29=-1
-7%2B6=-1
-1=-1
The solution was verified using both equations.
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Now the algebraic solution.
1.x%2B2y=9
2.-x%2B6y=-1
Add eq. 1 and eq. 2 to get rid of x.
x%2B2y%2B%28-x%29%2B6y=9-1
8y=8
highlight%28y=1%29
Then from eq. 1,
1.x%2B2y=9
x%2B2%281%29=9
highlight%28x=7%29