Section 5.1

문제 2

Determine whether the given ordered pair is a solution of the system. $open paren negative 3 comma 5 close paren$

$\begin{cases} 9x + 7y = 8 \\ 8x - 9y = -69 \end{cases}$

문제 7

In Exercises 5–18, solve each system by the substitution method. $\begin{cases} x + 3y = 8 \\ y = 2x - 9 \end{cases}$

문제 9

In Exercises 5–18, solve each system by the substitution method. $\begin{cases} x = 4y - 2 \\ x = 6y + 8 \end{cases}$

문제 51

Solve each system for x and y, expressing either value in terms of a or b, if necessary. Assume that a ≠ 0 and b ≠ 0. For the linear function f(x) = mx + b, f(−2) = 11 and ƒ(3) = -9. Find m and b.

Section 5.2

문제 1

Determine whether the given ordered pair is a solution of the system. $open paren 2 comma 3 close paren$

$\begin{cases} x + 3y = 11 \\ x - 5y = -13 \end{cases}$

문제 1

Solve each system by the substitution method.

$\begin{cases} x + y = 2 \\ y = x^2 - 4 \end{cases}$

문제 1

Determine if the given ordered triple is a solution of the system. $open paren 2 comma negative 1 comma 3 close paren$

$\begin{cases} x + y + z = 4 \\ x - 2y - z = 1 \\ 2x - y - 2z = -1 \end{cases}$

문제 3

Determine if the given ordered triple is a solution of the system. $open paren 4 comma 1 comma 2 close paren$

$\begin{cases} x - 2y = 2 \\ 2x + 3y = 11 \\ y - 4z = -7 \end{cases}$

문제 5

Solve each system in Exercises 5–18.

$\begin{cases} x + y + 2z = 11 \\ x + y + 3z = 14 \\ x + 2y - z = 5 \end{cases}$

문제 7

Solve each system in Exercises 5–18. $\begin{cases} 4x - y + 2z = 11 \\ x + 2y - z = -1 \\ 2x + 2y - 3z = -1 \end{cases}$

문제 9

Solve each system in Exercises 5–18. $\begin{cases} 3x + 2y - 3z = -2 \\ 2x - 5y + 2z = -2 \\ 4x - 3y + 4z = 10 \end{cases}$

문제 11

Solve each system in Exercises 5–18. $\begin{cases} 2x - 4y + 3z = 17 \\ x + 2y - z = 0 \\ 4x - y - z = 6 \end{cases}$

문제 13

Solve each system in Exercises 5–18. $\begin{cases} 2x + y = 2 \\ x + y - z = 4 \\ 3x + 2y + z = 0 \end{cases}$

문제 15

Solve each system in Exercises 5–18. $\begin{cases} x + y = -4 \\ y - z = 1 \\ 2x + y + 3z = -21 \end{cases}$

문제 17

Solve each system in Exercises 5–18. $\begin{cases} 3(2x + y) + 5z = -1 \\ 2(x - 3y + 4z) = -9 \\ 4(1 + x) = -3(z - 3y) \end{cases}$

문제 19

Find the quadratic function y = ax²+bx+c whose graph passes through the given points. (−1, 6), (1, 4), (2, 9)

문제 21

Find the quadratic function y = ax²+bx+c whose graph passes through the given points. (−1,−4), (1,−2), (2, 5)

문제 25

Solve each system in Exercises 25–26. $\begin{cases} \frac{x + 2}{6} - \frac{y + 4}{3} + \frac{z}{2} = 0 \\ \frac{x + 1}{2} + \frac{y - 1}{2} - \frac{z}{4} = \frac{9}{2} \\ \frac{x - 5}{4} + \frac{y + 1}{3} + \frac{z - 2}{2} = \frac{19}{4} \end{cases}$

문제 26

Solve each system in Exercises 25–26. $\begin{cases} \frac{x + 3}{2} - \frac{y - 1}{2} + \frac{z + 2}{4} = \frac{3}{2} \\ \frac{x - 5}{2} + \frac{y + 1}{3} - \frac{z}{4} = - \frac{25}{6} \\ \frac{x - 3}{4} - \frac{y + 1}{2} + \frac{z - 3}{2} = - \frac{5}{2} \end{cases}$

문제 57

Exercises 57–59 will help you prepare for the material covered in the next section. Subtract: $\frac{3}{x - 4} - \frac{2}{x + 2}$

문제 59

Exercises 57–59 will help you prepare for the material covered in the next section. Solve: $\begin{cases} A + B = 3 \\ 2A - 2B + C = 17 \\ 4A - 2C = 14 \end{cases}$

Section 5.3

문제 1

Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants.(11x - 10)/(x − 2) (x + 1)

문제 3

Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. $\frac{6 x^{2} - 14 x - 27}{(x + 2) (x - 3)^{2}}$

문제 5

Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. $\frac{5x^2 - 6x + 7}{(x - 1)(x^2 + 1)}$

문제 7

Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. $\frac{x^3 + x^2}{(x^2 + 4)^2}$

문제 9

Write the partial fraction decomposition of each rational expression. x/(x-2)(x-3)

문제 11

Write the partial fraction decomposition of each rational expression. (3x +50)/(x -9)(x +2)

문제 13

Write the partial fraction decomposition of each rational expression. (7x-4)/(x²-x-12)

문제 14

Write the partial fraction decomposition of each rational expression. 9x+21/(x² + 2x - 15)

문제 15

Write the partial fraction decomposition of each rational expression. 4/(2x² -5x -3)