2x-3y=7 15x+3y=10

To solve the system of equations:

1. \( 2x - 3y = 7 \) (Equation 1)
2. \( 15x + 3y = 10 \) (Equation 2)

We can use the elimination method or substitution method. Here, let's use the elimination method.

First, we can add both equations directly, but first, let's manipulate them a little to eliminate \( y \).

From Equation 1, we can express \( y \) in terms of \( x \): \[ 3y = 2x - 7 \quad \Rightarrow \quad y = \frac{2x - 7}{3} \]

Now we can plug this expression for \( y \) into Equation 2: \[ 15x + 3\left(\frac{2x - 7}{3}\right) = 10 \]

This simplifies to: \[ 15x + (2x - 7) = 10 \] \[ 17x - 7 = 10 \]

Now, add 7 to both sides: \[ 17x = 17 \]

Now, divide both sides by 17: \[ x = 1 \]

Now that we know \( x \), we can substitute it back into the equation for \( y \): \[ y = \frac{2(1) - 7}{3} = \frac{2 - 7}{3} = \frac{-5}{3} \]

So the solution to the system of equations is: \[ x = 1, \quad y = -\frac{5}{3} \]

Thus, the solution is \( (x, y) = (1, -\frac{5}{3}) \).