Question

1) The following are linear equations except…… A. 1 2 − + 3 = −1. B. 11 + = . C. 1√ + 2 = 3. D. 1 − 22 − 33 = 4. 2) The equation + = , (a,b not both 0), is homogeneous equation. (A. True B. False) 3) System of linear equations is a finite set of equations. (A. True B. False) 4) 5 + = 3 2 − = 4 be a system of linear equations. (A. True B. False) 5) 41 − 2 + 33 = −1 31 + 2 + 93 = −4 be a system of equations. (A. True B. False) 6) The following are systems of equations except …… A. 1 2 − + 3 = −1 − 2√ − 3 = 0 . B. 1 2 − + 3 = −1 − sin − = 0 + + = −1 . C. 1 2 − + 3 = −1 − 2 − 3 = 0 D. nothing of the previous 7) 11 + 12 = 1 21 + 22 = 2 be the general form for a system of linear equations. (A. True B. False) 8) 111 + 122 = 1 211 + 222 = 2 be the general form for a system of linear equations. (A. True B. False) 9) 51 + 2 = 10 111 + 32 = 2 be the general form for a system of linear equations. (A. True B. False) 10) All nonlinear equations cannot be transformed to linear one. (A. True B. False) 11) The nonlinear equation sin + cos = 1 can be transformed to linear. (A. True B. False) 12) The following equation can be represented as linear equations except…… A. ++ = 1. B. = 1. C. both choices A and B. D. neither choice A nor B. 13) A solution of a linear system is a sequence of numbers 1, 2, 3, … , . (A. True B. False) 14) = 1, = −2 be a solution of the system 5 + = 3 2 − = 4 . (A. True B. False)

Answer 1

This response explains linear equations, homogeneous equations, systems of linear equations, and whether given equations are linear or not.

Step-by-step explanation:

1) The linear equations in the given options are:

A. 12 - 2x + 3 = -1

B. 11 + y = x

C. 1√x + 2 = 3

D. 1 - 22y - 33 = 4

2) The equation y = ax + b is a linear equation, while y = a + bx (a, b not both 0) is a homogeneous equation. Therefore, the statement is false.

3) A system of linear equations is a finite set of equations. Hence, the statement is true.

4) The given set of equations is linear. Hence, the statement is true.

5) The given set of equations is linear. Hence, the statement is true.

6) The linear systems of equations are:

A. 12 - 2x + 3 = -1 and √x - 2y - 3 = 0

B. 12 - 2x + 3 = -1, sinx - y = 0, and x + y = -1

C. 12 - 2x + 3 = -1 and 1 - 2y - 3 = 0

The statement does not mention option D.

7) The given equations are not in the general form for a system of linear equations. Hence, the statement is false.

8) The given equations are not in the general form for a system of linear equations. Hence, the statement is false.

9) The given equations are not in the general form for a system of linear equations. Hence, the statement is false.

10) Nonlinear equations cannot always be transformed into linear ones. Hence, the statement is true.

11) The given equation sinx + cosy = 1 is nonlinear. Hence, the statement is false.

12) The equation that cannot be represented as a linear equation is A. x2 + y = 1. Neither choice A nor B represents the equation. Hence, the statement is false.

13) A solution of a linear system is a sequence of numbers 1, 2, 3, etc. The statement is false.

14) The given values x = 1 and y = -2 satisfy the system of linear equations 5x + y = 3 and 2x - y = 4. Hence, the statement is true.