find the simultaneous solution by graphing. (10 points)\nsupply is defined as the amount produced. demand is…

find the simultaneous solution by graphing. (10 points)\nsupply is defined as the amount produced. demand is defined as the amount consumers will purchase. define the y axis as price, the x axis as quantity.\nit has been determined that demand is denoted by: x + y = 6\nit has been determined that supply is denoted by: x - y = 2\ngraph the solution and label the point of intersection as the equilibrium point.

find the simultaneous solution by graphing. (10 points)\nsupply is defined as the amount produced. demand is defined as the amount consumers will purchase. define the y axis as price, the x axis as quantity.\nit has been determined that demand is denoted by: x + y = 6\nit has been determined that supply is denoted by: x - y = 2\ngraph the solution and label the point of intersection as the equilibrium point.

Answer

Explanation:

Step1: Rewrite equations in slope - intercept form

For demand $x + y=6$, rewrite as $y=-x + 6$. Here the slope $m_1=-1$ and y - intercept $b_1 = 6$. For supply $x - y=2$, rewrite as $y=x - 2$. Here the slope $m_2 = 1$ and y - intercept $b_2=-2$.

Step2: Find intersection point algebraically

Set the two equations equal: $-x + 6=x - 2$. Add $x$ to both sides: $6 = 2x-2$. Add 2 to both sides: $8 = 2x$. Divide by 2: $x = 4$. Substitute $x = 4$ into $y=-x + 6$, we get $y=-4 + 6=2$.

Answer:

The equilibrium point (point of intersection) is $(4,2)$