Math Problem Help plz!!!?

Question

Find the point of intersection of the lines y=2/3x-1 and 3x-4y=8

Answer 1

y = 2/3x - 1- - - - - - -Equation 1
3x - 4y = 9- - - - - - - Equation 2
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Convert equation 1 to standard form

y = 2/3x - 1

3(y) = 3(2/3)x - 3(1)

3y = 2x - 3

- 2x + 3y = 2x - 3 - 2x

- 2x + 3y = - 3. . . .Standard form Equation 1
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- 2x + 3y = - 3
3x - 4y = 8
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Multiply standard form equation 1 by 4 and equation 2 by 3

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- 2x + 3y = - 3

- 4(2)x + 4(3)y = - 4(3)

- 8x + 12y = - 12
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3x - 4y = 9
3(3x) - 3(4)y = 3(8)

9x - 12y = 24

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- 8x + 12y = - 12
9x + 12y = 24
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x = 12

The answer is x = 12

Insert the x value into equation 1
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y = 2/3x - 1

y = 2/3(12) - 1

y = 24/3 - 1

y = 8 - 1

y = 7

The answer is y = 7

Insert the y value into equation 1

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Check for equation 1

y = 2/3x - 1

7 = 2/3(12) - 1

7 = 24/3 - 1

7 = 8 - 1

7 = 7

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Check for equation 2

3x - 4y = 8

3(12) - 4(7) = 8

36 - 28 = 8

8 = 8

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The solution set { 12, 7)

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Answer 2

Treat it like a simultaneous equation:

there are 3 ways to solve these just use which ever is easier in the cicumstances:

1) make both =y (i tried this but u get fractions and i dnt like them)
2) shove value of y into other equation
y=2/3x-1 and 3x-4y=8
3x-4(2/3-1)=8
3x-(2 and 2/3)-4=8
3x=8+(2 and 2/3)-4
3x=4 +2 and 2/3
3x=6 and 2/3
x=6 and 2/3 (divided by 3)
which my calculator says is 2 and 2/9 then work out y by shoving this x value into one of the line equations
3)use simultaneous method (not practical in this cirumstance)

Answer 3

2/(3x-1) = (8-3x)/4

8 = (8-3x)(3x-1)

24x-9x^2-8+3x - 8 = 0

27x - 9x^2 - 16 = 0

Solve for x and substitute in the values for y

Answer 4

3x-4y=8
-4y=-3x+8
y=3/4x-2
now you set the equations equl with each other
2/3x-1=3/4x-2
2/3x-3/4x=-1
8/12x-9/12x=-1
-1/12x=-1
x=12
now you plug in 12 in one of the equation
y=2/3*12-1
y=7
(12,7) point of intersection

Answer 5

the method that samuel d used is the easiest because there are no fractions to worry about. systems are really easier to work with when you eliminate the factions. the solution is ( 12, 7 )