Solving a system of linear equations with fractional coelilcients Solve the following system of equations. \[ \begin{array}{l} \frac{1}{5} x-\frac{1}{4} y=-1 \\ -\frac{3}{4} x+\frac{1}{2} y=-5 \end{array} \] \[ \begin{array}{l} x= \\ y= \end{array} \]

Step 1 ：Given the system of equations: \[\frac{1}{5} x-\frac{1}{4} y=-1\] and \[-\frac{3}{4} x+\frac{1}{2} y=-5\]

Step 2 ：First, eliminate the fractions by multiplying each equation by the least common multiple (LCM) of the denominators. This transforms the system of equations into: \[4.0x - 5.0y = -20\] and \[-15.0x + 10.0y = -100\]

Step 3 ：Next, use the elimination method to solve the system. This gives the solution: \[x = 20.0000000000000\] and \[y = 20.0000000000000\]

Step 4 ：Thus, the solution to the system of equations is \[x = \boxed{20}\] and \[y = \boxed{20}\]