After clearing fractions, you will have two equations with integer coefficients. Choose elimination: multiply the equations so that either the x-terms or the y-terms become opposites, then add the equations.

Once you find x and y, plug them into 3x − 2y. Do not stop there—remember the question is asking for 13(3x − 2y), so you need one more multiplication.

In Desmos, enter the first equation exactly as given: (3/4)x - (2/5)y = 1. On a new line, enter the second equation: (1/2)x + (3/5)y = 4. Desmos can graph these implicit equations.

Look for the point where the two lines intersect. Tap or click that intersection; Desmos will display approximate coordinates for $(x, y)$ of the solution to the system.

Using the x- and y-values from the intersection (rounded to a few decimal places), type a new expression in Desmos like 13*(3*X - 2*Y), replacing X and Y with the numerical intersection coordinates you read. The calculator will show a value very close to an integer; that integer is the value you should report.

The original system is

The least common multiple of 4, 5, and 2 is 20. Multiply each equation by 20 to remove denominators.

First equation:

This simplifies to

Second equation:

This simplifies to

So the equivalent system (with no fractions) is

Work with the system

Eliminate $x$ by making the $x$-coefficients opposites.

Multiply equation (1) by 2:

Multiply equation (2) by $-3$:

Now add these two new equations:

which gives

Solve for $y$:

Use equation (2): $10x + 12y = 80$.

Substitute $y = \frac{50}{13}$:

Compute the product:

So

Write 80 with denominator 13:

so

Therefore

So the solution to the system is

First find $3x - 2y$ using $x = \frac{44}{13}$ and $y = \frac{50}{13}$:

Compute each term:

So

Now multiply by 13:

The requested value is $32$.