Solve the problem.
-Use inverse matrices to find the equilibrium point for the demand and supply curves below.
$p = 100 - 10 x \quad$ Demand curve
$p = 30 + 5 x \quad$ Supply curve
A) $\left( \frac { 20 } { 3 } , \frac { 190 } { 3 } \right)$
B) $( 70,380 )$
C) $\left( \frac { 14 } { 3 } , \frac { 160 } { 3 } \right)$
D) $\left( \frac { 26 } { 3 } , \frac { 220 } { 3 } \right)$

Question

Quizplus · Accepted Answer

To find the equilibrium point, set the demand and supply equations equal: $100 - 10x = 30 + 5x$. Solving for $x$, we get $x = \frac{14}{3}$. Substitute $x$ back into either equation to find $p$: $p = 100 - 10(\frac{14}{3}) = \frac{160}{3}$. Thus, the equilibrium point is $\left( \frac{14}{3}, \frac{160}{3} \right)$.

Solve the Problem p=100−10xp = 100 - 10 x \quadp=100−10x Demand Curve

Solve the Problem $p = 100 - 10 x \quad$ Demand Curve