if 3p-q=6 and 2p+3q=4 find the value of p and q
You asked:
Given \( 3 p - q = 6 \), \( 2 p + 3 q = 4 \), evaluate \( p \), \( q \).
MathBot Answer:
The system of linear equations has exactly one solution.
The substitutions are \( p = 2 \), \( q = 0 \).
\[p = 2\]
\[q = 0\]
Solve \(3 p - q = 6\) for \(p\). \[p = \frac{q}{3} + 2\]
Substitute \(\frac{q}{3} + 2\) for \(p\) in \(2 p + 3 q = 4\) and simplify. $$\begin{aligned}2 p + 3 q &= 4 \\ 2 \left(\frac{q}{3} + 2\right) + 3 q &= 4 \\ q &= 0 \end{aligned}$$
Use substitution of the numerical value of \(q\) to get the values of \(p\). $$\begin{aligned}p &= \frac{q}{3} + 2 \\ p &= \frac{0}{3} + 2 \\ p &= 2\end{aligned}$$