.{2(x-y)-7x=13 {15x+3(x+y)=-9

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

The equations you provided are:

1. \( 2(x - y) - 7x = 13 \)
2. \( 15x + 3(x + y) = -9 \)

Step 1: Simplifying the First Equation

Starting with the first equation: \[ 2(x - y) - 7x = 13 \] Distributing \(2\): \[ 2x - 2y - 7x = 13 \] Combining like terms: \[ -5x - 2y = 13 \] Rearranging it gives: \[ 5x + 2y = -13 \quad \text{(1)} \]

Step 2: Simplifying the Second Equation

Now, let's simplify the second equation: \[ 15x + 3(x + y) = -9 \] Distributing \(3\): \[ 15x + 3x + 3y = -9 \] Combining like terms: \[ 18x + 3y = -9 \] Rearranging it gives: \[ 6x + y = -3 \quad \text{(2)} \]

Step 3: Solving the System of Equations

Now we have the system:

1. \( 5x + 2y = -13 \)
2. \( 6x + y = -3 \)

We can express \(y\) from equation (2): \[ y = -3 - 6x \quad \text{(3)} \]

Now, substitute (3) into (1): \[ 5x + 2(-3 - 6x) = -13 \] Distributing: \[ 5x - 6 - 12x = -13 \] Combining like terms: \[ -7x - 6 = -13 \] Adding \(6\) to both sides: \[ -7x = -7 \] Dividing by \(-7\): \[ x = 1 \]

Step 4: Finding \(y\)

Now substitute \(x = 1\) back into equation (3): \[ y = -3 - 6(1) \] Calculating: \[ y = -3 - 6 = -9 \]

Final Solution

Thus, the solution to the system of equations is: \[ x = 1, \quad y = -9 \]

You can confirm this solution by substituting \(x = 1\) and \(y = -9\) back into the original equations.