Questions on Algebra: Linear Algebra (NOT Linear Equations) answered by real tutors!

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


thanks in advance: 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(1798) 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+2y=9
2y=9-x
y=(9-x)/2
Slope = -1/2, Y-intercept=9/2
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-x+6y=-1
6y=x-1
y=(x-1)/6
Slope=1/6, Y-intercept=-1/6
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Then graph the two lines.
drawing( 300, 300, -2, 10, -5, 5,grid( 1 ),circle( 7, 1, .2 ), graph( 300, 300, -2, 10, -5, 5, (9-x)/2, (x-1)/6))
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Looks like (7,1) is the solution.
Check using the equations.
x+2y=9
7+2(1)=9
7+2=9
9=9
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-x+6y=-1
-7+6(1)=-1
-7+6=-1
-1=-1
The solution was verified using both equations.
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Now the algebraic solution.
1.x+2y=9
2.-x+6y=-1
Add eq. 1 and eq. 2 to get rid of x.
x+2y+(-x)+6y=9-1
8y=8
highlight(y=1)
Then from eq. 1,
1.x+2y=9
x+2(1)=9
highlight(x=7)