Fill in each blank so that the resulting statement is true. When solving { x = 3 y + 2 5 x − 15 y = 10 by the substitution method, we obtain 10 = 10 , so the solution set is_______________________ The equations in this system are called _______ If you attempt to solve such a system by graphing, you will obtain two lines that ______________.
Fill in each blank so that the resulting statement is true. When solving { x = 3 y + 2 5 x − 15 y = 10 by the substitution method, we obtain 10 = 10 , so the solution set is_______________________ The equations in this system are called _______ If you attempt to solve such a system by graphing, you will obtain two lines that ______________.
Solution Summary: The author explains that the equations in a linear equation are called dependent, which means the system has infinite solutions and the lines are coincident.
Fill in each blank so that the resulting statement is true.
When solving
{
x
=
3
y
+
2
5
x
−
15
y
=
10
by the substitution method, we obtain
10
=
10
, so the solution set is_______________________ The equations in this system are called _______ If you attempt to solve such a system by graphing, you
(20 p) 1. Find a particular solution satisfying the given initial conditions for the third-order
homogeneous linear equation given below. (See Section 5.2 in your textbook if you need a
review of the subject.)
y(3)+2y"-y-2y = 0; y(0) = 1, y'(0) = 2, y"(0) = 0;
y₁ = e*, y2 = e¯x, y3 = e−2x
(20 p) 2. Find a particular solution satisfying the given initial conditions for the second-order
nonhomogeneous linear equation given below. (See Section 5.2 in your textbook if you need
a review of the subject.)
y"-2y-3y = 6; y(0) = 3, y'(0) = 11
yc = c₁ex + c2e³x; yp = −2
(60 p) 3. Find the general, and if possible, particular solutions of the linear systems of
differential equations given below using the eigenvalue-eigenvector method. (See Section
7.3 in your textbook if you need a review of the subject.)
=
a) x 4x1 + x2, x2 = 6x1-x2
b) x=6x17x2, x2 = x1-2x2
c) x = 9x1+5x2, x2 = −6x1-2x2; x1(0) = 1, x2(0)=0
4. In a study of how students give directions, forty volunteers were given the task ofexplaining to another person how to reach a destination. Researchers measured thefollowing five aspects of the subjects’ direction-giving behavior:• whether a map was available or if directions were given from memory without a map,• the gender of the direction-giver,• the distances given as part of the directions,• the number of times directions such as “north” or “left” were used,• the frequency of errors in directions.a) Identify each of the variables in this study, and whether each is quantitative orqualitative. For each quantitative variable, state whether it is discrete or continuousb) Was this an observational study or an experimental study? Explain your answer
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