The solution is: (6,0)
Step-by-step explanation:
Given equations are:
[tex]x+6y = 6\\y = \frac{1}{3}x-2[/tex]
Part A:
The graph is made using the online tool Desmos.
The graph is attached as a picture
Part B: Solution from graph:
On the graph we can see that both lines intersect at (6,0)
So the solution is x=6 and y=0
Part C: Algebraic Verification
[tex]x+6y = 6\ \ \ \ Eqn1\\y = \frac{1}{3}x-2\ \ \ \ Eqn2[/tex]
Putting y= 1/3x-2 in equation 1
[tex]x+ 6(\frac{1}{3}x-2) = 6\\x + 2x-12 = 6\\3x -12 = 6[/tex]
Adding 12 on both sides
[tex]3x-12+12 = 6+12\\3x = 18[/tex]
Dividing both sides by 3
[tex]\frac{3x}{3} = \frac{18}{3}\\x = 6[/tex]
Putting x = 6 in equation 2
[tex]y = \frac{1}{3}(6)-2\\y = 2-2\\y = 0[/tex]
Hence,
The solution is: (6,0)
Keywords: Graphing, linear equations
Learn more about linear equations at:
- brainly.com/question/10666510
- brainly.com/question/10699220
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