System of linear equations and Quadratic Functions, math homework help

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MATH 140 College Algebra Quiz 5 Student Name _____________________________________ Section ___ Date _______ Systems of Linear Equations, Matrices and Determinants Select the correct answer or enter the answers in the spaces provided. (1) __________ Solve the system of linear equations by substitution. + x + 4 y = + 13 − x − 3 y = − 11 (2) __________ Solve the system of linear equations by elimination. 1x + 4y = 2 2x − 1y = 1 (3) __________ Determine the Quadrant, in the Cartesian Coordinate System, that contains the solution to this system. 3 x + 5 y = + 20 1 x + 7 y = − 14 Also, sketch the graph of the system using the provided coordinate grid. Label the axes and scale the grid accordingly. Label the point of intersection. (4) __________ For this linear system, determine the determinant of the matrix of coefficients. + 2 a − 3 b = 06 − 2 a + 3 b = 12 (5) __________ Find the equilibrium point for this demand and supply equation system, where p is the price and x is the number of units that satisfy both the demand and supply equations. p = $ 400 − $ 0.002 x p = $ 225 + $ 0.005 x (c) Copyright 2017 by P . E . P . Form A demand equation supply equation 1 MATH 140 College Algebra Quiz 5 Student Name _____________________________________ Section ___ Date _______ (6) __________ When using Cramer’s Rule to solve the given system of linear equations, what would be the determinant D x of the numerator in the solution for the x variable only? +1x − 4y = 9 − 3 x = 12 y − 30 (7) __________ Determine whether the system has one solution, no solution or an infinite number of solutions. 1 m + 3 n = 06 1 m + 2 n = 12 __________ Determine whether the system has one solution, no solution or an infinite number of solutions. 1 m + 3 n = 06 1 m + 3 n = 12 __________ Determine whether the system has one solution, no solution or an infinite number of solutions. 3 m + 2 n = 06 6 m + 4 n = 12 (8) __________ Evaluate the following 3 by 3 determinant. +2 +0 −3 (9) __________ −1 +8 +5 +4 +1 +6 Solve this 3 by 3 system of linear equations. − 4 u + 7 v − 10 w = + 35 + 5 u + 5 v − 02 w = + 09 + 2 u − 3 v − 04 w = − 41 (10) __________ Solve the 3 by 3 system of linear equations. + 1 u + 10 v = − w + 52 − 5 u = v + 4 w − 15 + 1 u + 2 v − 3 w = 12 (c) Copyright 2017 by P . E . P . Form A 2
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MATH 140 College Algebra

Quiz 5

Student Name _____________________________________ Section ___ Date _______

Systems of Linear Equations, Matrices and Determinants
Select the correct answer or enter the answers in the spaces provided.
(1)

(5, 2)

Solve the system of linear equations by substitution.
+ x + 4 y = + 13
− x − 3 y = − 11

(5, 2)
(2)

(2/3, 1/3)

(2/3, 1/3)

Solve the system of linear equations by elimination.
1x + 4y = 2
2x − 1y = 1

(3) (105/8, -31/8), Quadrant IV
Determine the Quadrant, in the Cartesian Coordinate System, that
contains the solution to this system.
3 x + 5 y = + 20
1 x + 7 y = − 14
(105/8, -31/8) Quadrant IV
Also, sketch the graph of the system using the provided
coordinate grid. Label the axes and scale the grid accordingly.
Label the point of intersection.

(c) Copyright 2017 by P . E . P .

Form A

1

MATH 140 College Algebra

Quiz 5

Student Name _____________________________________ Section ___ Date _______

(4)

0

For this linear system, determine the deter...


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