solve each system by graphing both equations on the same set of axes and then reading the solution from graph?

Question

y = 2/3x
y = - 1/3 x + 6

Answer 1

y = 2/3x- - - - - -- - Equation 1
y = - 1/3x + 6- - - -Equation 2
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Convet equation 2 to standard form

y = - 1/3x + 6

1/3x + y = 6

3(1/3x) + 3(y) = 3(6)

x + 3y = 18. . .standard form
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Insert the y value of equation 1 into the standard form equation.

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x + 3y = 18

x + 3(2/3x) = 18

x + 6/3x = 18

x + 2x = 18

3x = 18

3x/3 = 18/3

x = 18/3

x = 6

The answer is x = 6

Insert the x value into equation 2

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y = - 1/3x + 6

y = - 1/3(6) + 6

y = - 6/3 + 6

y = - 2 + 6

y = 4

The answer y = 4

Insert the y value into equation 2

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Check for equation 2

y = - 1/3x + 6

4 = - 1/3(6) + 6

4 = - 6/3 + 6

4 = - 2 + 6

4 = 4

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Check for equation 1

y = 2/3x

4 = 2/3(6)

4 = 12/3

4 = 4

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The solution set is { 6, 4 }

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Answer 2

Take 2/3x and put it in the place of y:
2/3x=-1/3x+6

Multiply both sides by 3 to get rid of the fractions:
2x=-x+18

Add x from both sides:
3x=18

Divide 3 from both sides:
x=6

y=2/3(6)
y=2(2)
y=4

y=-1/3(6)+6
y=-2+6
y=4

The solution set is (6,4)

Check:
4=2/3(6)
4=12/3
4=4

4=-1/3(6)+6
4=-2+6
4=4

I hope this helps!

Answer 3

You can graph these and see where they intersect or since they are both equal to y they are equal to one another.

2/3x = -1/3x+ 6
x = 6

y = 4