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.