Solve the system of equations: 2y + 2x = 69.48 y + 12.8 = x

Let's solve the system of equations step by step:

The given system is:

$$ \begin{cases} 2y + 2x = 69.48 \\ y + 12.8 = x \end{cases} $$

Step 1: Substitute the value of x from the second equation into the first equation.

From the second equation, we have ( x = y + 12.8 ). Substitute this into the first equation:

$$ 2y + 2(y + 12.8) = 69.48 $$

Step 2: Simplify and solve for y.

Expand and simplify the equation:

$$ 2y + 2y + 25.6 = 69.48 $$ $$ 4y + 25.6 = 69.48 $$

Subtract 25.6 from both sides:

$$ 4y = 69.48 - 25.6 $$ $$ 4y = 43.88 $$

Divide by 4 to find the value of y:

$$ y = \frac{43.88}{4} $$ $$ y = 10.97 $$

Step 3: Substitute the value of y back into the second equation to find x.

We have ( x = y + 12.8 ), and now we know ( y = 10.97 ), so:

$$ x = 10.97 + 12.8 $$ $$ x = 23.77 $$

Step 4: Write the final answer.

The solution to the system of equations is ( x = 23.77 ) and ( y = 10.97 ).

Answer: x = 23.77, y = 10.97