Solving a system of linear equations with fractional coelilcients
Solve the following system of equations.
\[
\begin{array}{l}
\frac{1}{5} x-\frac{1}{4} y=-1 \\
-\frac{3}{4} x+\frac{1}{2} y=-5
\end{array}
\]
\[
\begin{array}{l}
x= \\
y=
\end{array}
\]
Answer
Thus, the solution to the system of equations is \[x = \boxed{20}\] and \[y = \boxed{20}\]
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 \[y = \boxed{20}\]
