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3y=5x+6 and 3y-5x=8. Solve the system of equations.

User Mindvision
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Answer: 1/6

Step-by-step explanation: To solve the system of equations:

3y = 5x + 6 (equation 1)

3y - 5x = 8 (equation 2)

We can use substitution method or elimination method.

Substitution method:

From equation 1, we have:

3y = 5x + 6

y = (5/3)x + 2 (divide both sides by 3)

Substitute y in equation 2 with (5/3)x + 2:

3y - 5x = 8

3((5/3)x + 2) - 5x = 8

5x + 6 - 5x = 8

6 = 8

The equation 6=8 is not true, which means there is no solution that satisfies both equations.

Elimination method:

Multiply equation 1 by 5:

15y = 25x + 30 (equation 1 multiplied by 5)

Subtract equation 2 from equation 1:

15y - (3y - 5x) = 25x + 30 - 8

12y + 5x = 22

Simplify:

12y = -5x + 22

y = (-5/12)x + 11/6

Now substitute y in equation 1 with (-5/12)x + 11/6:

3((-5/12)x + 11/6) = 5x + 6

(-5/4)x + 11 = 5x + 6

11 - 6 = 5x + (5/4)x

5/4 x = 5

x = 4

Now substitute x = 4 in y = (-5/12)x + 11/6:

y = (-5/12)(4) + 11/6

y = -5/3 + 11/6

y = 1/6

Therefore, the solution to the system of equations is x = 4 and y = 1/6.

User Sivasankar
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