Repeat Problem 63 for the following systems: A 6 x − 5 y = 10 ( B ) 6 x − 5 y = 10 − 13 + 11 y = − 20 11 x + 8 y = 4 C 6 x − 5 y = 10 − 12 x + 10 y = − 20 bushels, and the annual demand is 2.0 billion bushels. When the price increases to $ 5.10 per bushel, the annual supply in-creases to 2.1 billion bushels, and the annual demand decreases to 1.8 billion bushels. Assume that the price-supply and price-demand equations are linear. (A) Find the price-supply equation. (B) Find the price-demand equation. (C) Find the equilibrium price and quantity. (D) Graph the two equations in the same coordinate system and identify the equilibrium point, supply curve, and demand curve.
Repeat Problem 63 for the following systems: A 6 x − 5 y = 10 ( B ) 6 x − 5 y = 10 − 13 + 11 y = − 20 11 x + 8 y = 4 C 6 x − 5 y = 10 − 12 x + 10 y = − 20 bushels, and the annual demand is 2.0 billion bushels. When the price increases to $ 5.10 per bushel, the annual supply in-creases to 2.1 billion bushels, and the annual demand decreases to 1.8 billion bushels. Assume that the price-supply and price-demand equations are linear. (A) Find the price-supply equation. (B) Find the price-demand equation. (C) Find the equilibrium price and quantity. (D) Graph the two equations in the same coordinate system and identify the equilibrium point, supply curve, and demand curve.
Solution Summary: The author explains how to determine whether the solution set for the three equations is nearly identical, graphically and by using substitution or elimination by addition.
A
6
x
−
5
y
=
10
(
B
)
6
x
−
5
y
=
10
−
13
+
11
y
=
−
20
11
x
+
8
y
=
4
C
6
x
−
5
y
=
10
−
12
x
+
10
y
=
−
20
bushels, and the annual demand is
2.0
billion bushels. When the price increases to
$
5.10
per bushel, the annual supply in-creases to
2.1
billion bushels, and the annual demand decreases to
1.8
billion bushels. Assume that the price-supply and price-demand equations are linear.
(A) Find the price-supply equation.
(B) Find the price-demand equation.
(C) Find the equilibrium price and quantity.
(D) Graph the two equations in the same coordinate system and identify the equilibrium point, supply curve, and demand curve.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
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For problems 3-10, solve the following systems using either substitution o
J lla – 7b -14
-8r +3s 10
4.
10r - 2s -2
3.
la-2b -4
6
= 8
13x +20y -1
5.
6.
19x 15y 87
15
14
= 21
5x +2y 10
5x +2y 11
7.
8.
5x + 2y 20
le+y3D4
3x+2y 8
10.
2x y 10
S 4x 2y 16
9.
y = 2x-8
Question 1
In each of Problems 1 through 8, express the general solution of the given system of equations in
terms of real-valued functions:
x₁ =
1. x2
Iz
=
2x₁ + 2x2 + x3
-2x1 + 2x2 + 2x3
2x₁3x₂-3x3
16) Solve the following system of equations for x:
y = 3x - 1
2x - y = 4
a. x = -10
b. x = -3
c. x = 5
d. x = -5
e. x = 3
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
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