4x+7y=39−1 2(x−y)=3x+y−2

Distribute the 2 on the left side and then rearrange the terms to group $x$ and $y$.

$$2x - 2y = 3x + 7y$$

Subtract $3x$ from both sides:

$$2x - 3x - 2y = 7y$$ $$-x - 2y = 7y$$

Add $2y$ to both sides:

$$-x = 7y + 2y$$ $$-x = 9y$$

Multiply by $-1$ to express $x$ in terms of $y$:

$$x = -9y$$

Substitute $x = -9y$ into $4x + 7y = 39$:

$$4(-9y) + 7y = 39$$

$$-36y + 7y = 39$$ $$-29y = 39$$

Divide by $-29$:

$$y = -\frac{39}{29}$$

$$x = -9\left(-\frac{39}{29}\right)$$ $$x = \frac{9 \times 39}{29}$$ $$x = \frac{351}{29}$$

The solution to the system of equations is:

$$x = \frac{351}{29}, y = -\frac{39}{29}$$