Question15. Find a value of $p$ that will result in one solution for this system. Then find the solution. $$\begin{array}{l} 3 x+y=-2 \\ p x-y=-12 \end{array}$$

Studdy Solution
Substitute $p = 0$ into the second equation and solve the system:
The system becomes:
1. $3x + y = -2$
2. $0 \cdot x - y = -12$ which simplifies to $-y = -12$ or $y = 12$
Substitute $y = 12$ into the first equation: $$3x + 12 = -2$$ $$3x = -2 - 12$$ $$3x = -14$$ $$x = -\frac{14}{3}$$
The solution to the system is: $$x = -\frac{14}{3}, \quad y = 12$$
The value of $p$ that results in one solution is any value except $-3$. For $p = 0$, the solution is $\left( -\frac{14}{3}, 12 \right)$.