Final answer:
By solving one equation for one variable and substituting it into the other equation, we find that the solution is x = 3/11 and y = -88/33.
Step-by-step explanation:
To solve the system of linear equations, we can use the method of substitution. First, solve one equation for one variable in terms of the other variable.
From the first equation, we have y = 1}/{3} - 3x. Substitute this value of y into the second equation and solve for x:
2x - 3(1}/{3} - 3x) = 8}/{3}
Next, solve for x:
2x - 1}/{3} + 9x = 8}/{3}
Combine like terms:
11x - 1}/{3} = 8}/{3}
Add 1}{3} to both sides:
11x = 9}/{3}
Divide both sides by 11:
x = 9}/{3} ÷ 11
So, x = 3}/{11}
Substitute this value of x back into one of the original equations and solve for y:
3(3}/{11}) + y = 1}/{3}
Multiply:
9}/{11} + y = 1}/{3}
Subtract 9}{11} from both sides:
y = 1}/{3} - 9}/{11}
Find a common denominator:
y = 1}/{3} - 9}/{11} × 11}/{11}
y = 11}/{33} - 99}/{33}
Combine like terms:
y = -88/}{33}
So, the solution to the system of linear equations is x = 3}/{11} and y = -88}/{33}.