Question

system of equations: p = 6 - 2q p = 4 + q note: use the orange line (square symbols) to plot the first equation, and use the blue line (circle symbols) to plot the second equation. the values of p and q that solve these two equations simultaneously can be seen on the graph as

Explanation:

Step1: Set the two equations equal

Since both $p = 6 - 2q$ and $p = 4+q$, we can set $6 - 2q=4 + q$.

Step2: Solve for q

Add $2q$ to both sides: $6=4 + q+2q$, which simplifies to $6 = 4+3q$. Then subtract 4 from both sides: $6 - 4=3q$, so $2 = 3q$. Divide both sides by 3, we get $q=\frac{2}{3}$.

Step3: Solve for p

Substitute $q = \frac{2}{3}$ into the second - equation $p = 4+q$. Then $p=4+\frac{2}{3}=\frac{12 + 2}{3}=\frac{14}{3}$.

Answer:

$p=\frac{14}{3},q=\frac{2}{3}$