Solve This Equation System: 2x - 1/5y = 18 and 3x + y = 6

Solve the following system of equations:

$\begin{cases} 2x-\frac{1}{5}y=18 \\ 3x+y=6 \end{cases}$

To solve the given system of equations using elimination, we'll follow these steps:

• Step 1: Simplify the first equation to remove the fraction.
• Step 2: Make the coefficients of $y$ in both equations equal, to facilitate elimination.
• Step 3: Eliminate $y$ by subtracting the equations.
• Step 4: Solve for $x$.
• Step 5: Use the value of $x$ to find the value of $y$.

Step 1: Multiply the first equation by 5 to clear the fraction:

$10x - y = 90$

Step 2: The second equation is already in a suitable form for elimination:

$3x + y = 6$

Step 3: Add the two equations:

$(10x - y) + (3x + y) = 90 + 6$

This simplifies to:

$13x = 96$

Step 4: Solve for $x$:

$x = \frac{96}{13} = 7.38$

Step 5: Substitute $x = 7.38$ back into the second equation to find $y$:

Edit Form|li $3(7.38) + y = 6$

$22.14 + y = 6$

$y = 6 - 22.14$

$y = -16.14$

Therefore, the solution to the system of equations is $x = 7.38$, $y = -16.14$.