Solve the system x + y = -1 and 3x - 2y = 7.

Step-by-step solution

1. 1

   Pick the easiest variable to isolate. In $x + y = -1$ both coefficients are $1$, so solving for either variable costs no fractions. Take

   $y = -1 - x$

2. 2

   Substitute into the second equation.

   $3x - 2(-1 - x) = 7$

   Distributing the $-2$ across both terms gives $+2$ and $+2x$:

   $3x + 2 + 2x = 7$

3. 3

   Solve the resulting single equation.

   $5x + 2 = 7 \quad\Longrightarrow\quad 5x = 5 \quad\Longrightarrow\quad x = 1$

4. 4

   Back-substitute to find y.

   $y = -1 - 1 = -2$

5. 5

   Check both original equations. $1 + (-2) = -1$ and $3(1) - 2(-2) = 3 + 4 = 7$. Both hold, so $(x, y) = (1, -2)$ is the unique intersection point of the two lines — unique because their slopes, $-1$ and $\tfrac32$, differ.