Solve the System: Using Substitution in 3x - 2y and 4x + 3y Equations

To solve the given system of equations using substitution, follow these steps:

First, we simplify the given equations. Let's start with the first equation:

Find a common denominator for fractions on the left side. The common denominator of 8 and 2 is 8:

Simplify inside the fraction:

This is our simplified form for the first equation.

Now, simplify the second equation:

Find a common denominator for the fractions, which is 15:

Distribute and simplify:

Multiply through by 15 to clear the fraction:

Now, we have two simplified equations:

From the first equation, solve for $x$:

Substitute $x = \frac{6y + 112}{7}$ into the second equation:

Distribute:

Clear the fraction by multiplying through by 7:

Combine like terms:

Subtract 224 from both sides:

Now, substitute $y \approx 12.93$ back into $x = \frac{6y + 112}{7}$:

Therefore, the solution to the system is:

$x \approx 27.08, \, y \approx 12.93$.

This corresponds to choice 1:

$x = 27.08, y = 12.93$.