Master Linear Equations: Enhance Your Math Skills for Pharmacy

Question 1

Solve the equation: 3x + 5 = 14

Accepted Answer

x = 3

Answer

x = 4

Answer

x = 5

Answer

x = 6

Question 2

Find the value of y that satisfies the equation: 2x - y = 6, given that x = 2

Accepted Answer

y = 4

Answer

y = 2

Answer

y = 6

Answer

y = 8

Question 3

Which of the following is the graph of the equation y = 2x + 1?

Accepted Answer

A straight line passing through the origin with a slope of 2

Answer

A parabola opening upwards with vertex at (0, 1)

Answer

A circle with radius 1 centered at (0, 1)

Answer

An ellipse with center at (0, 1)

Question 4

Find the determinant of the matrix: [[2, 3], [4, 5]]

Accepted Answer

6

Answer

-2

Answer

2

Answer

-6

Question 5

Which of the following is the inverse of the matrix: [[1, 2], [3, 4]]?

Accepted Answer

[[4, -2], [-3, 1]]

Answer

[[1, -2], [-3, 4]]

Answer

[[4, -2], [-1, 3]]

Answer

The matrix does not have an inverse.

Question 6

Which of the following matrices represents a rotation of -90 degrees clockwise?

Accepted Answer

[[0, -1], [-1, 0]]

Answer

[[0, 1], [1, 0]]

Answer

[[1, 0], [0, 1]]

Answer

[[1, 0], [0, -1]]

Question 7

Find the eigenvalues of the matrix: [[2, 1], [-1, 2]]

Accepted Answer

1, 3

Answer

2, 1

Answer

-1, -3

Answer

-2, -1

Question 8

Which of the following is the slope of the line represented by the equation y = -2x + 5?

Accepted Answer

-2

Answer

2

Answer

5

Answer

-5

Question 9

Which of the following is the inverse of the matrix A = [[1, 2], [3, 4]]?

Accepted Answer

[[4, -2], [-3, 1]]

Answer

[[-4, 2], [3, -1]]

Answer

[[2, -4], [-3, 1]]

Answer

[[-2, 4], [3, -1]]

Question 10

Identify the option that is NOT a type of linear equation:

Accepted Answer

Quadratic equation (ax² + bx + c = 0)

Answer

Standard form (Ax + By = C)

Answer

Point-slope form (y - y1 = m(x - x1))

Answer

Slope-intercept form (y = mx + c)

Question 11

Find the slope of a line perpendicular to the line with equation y = 3x + 2:

Accepted Answer

-1/3

Answer

1/3

Answer

-3

Answer

3

Question 12

Identify the matrix that is NOT invertible:

Accepted Answer

|0 1| |1 0|

Answer

|2 1| |3 2|

Answer

|1 2| |2 1|

Answer

|1 0| |0 1|

Question 13

What is the equation of the line that passes through the points (2, 3) and (-1, 5)?

Accepted Answer

y = -2x + 7

Answer

y = -x + 5

Answer

y = x + 1

Answer

y = 2x + 1

Question 14

Calculate the determinant of the matrix: 
 [[2, 3], [-1, 4]]

Accepted Answer

11

Answer

7

Answer

5

Answer

9

Question 15

Which of the following accurately describes the graph of a linear equation?

Accepted Answer

A straight line

Answer

An ellipse

Answer

A parabola

Answer

A circle

Question 16

What is the slope of the line perpendicular to the line represented by the equation y = 2x + 5?

Accepted Answer

-1/2

Answer

1/2

Answer

2

Answer

-2

Question 17

Solve for 'y' in the equation: 3(x + 2y) = 12

Accepted Answer

y = 2 - (x/2)

Answer

y = (x/2) + 2

Answer

y = 2(x - 2)

Answer

y = x/2 - 2

Question 18

What is the solution for 'x' in the equation: 2x + 5 = 13?

Accepted Answer

x = 4

Answer

x = 6

Answer

x = 8

Answer

x = 2

Question 19

Solve for 'y' in the equation: 3y - 7 = 16

Accepted Answer

y = 7

Answer

y = 3

Answer

y = 5

Answer

y = 9

Question 20

Find the values of 'x' and 'y' that satisfy the following system of equations: 
 2x + y = 5 
 x - y = 1

Accepted Answer

x = 2, y = 1

Answer

x = -2, y = -1

Answer

x = 2, y = -1

Answer

x = 1, y = 2

Question 21

Which of the following points is NOT a solution to the system of equations: 
 x + 2y = 6 
 3x - y = 5?

Accepted Answer

(1, 2)

Answer

(2, 1)

Answer

(0, 3)

Answer

(3, 0)

Question 22

Determine the determinant of the matrix: 
 [[2, 3], [-1, 4]]

Accepted Answer

11

Answer

5

Answer

9

Answer

7

Question 23

Which of the following is the inverse of the matrix: | 1 2 | | 3 4 |?

Accepted Answer

|-2 1| |1 -0.5|

Answer

|3 4| |1 2|

Answer

|1 2| |-3 -4|

Answer

|2 -1| |-1 0.5|

Question 24

Solve the system of equations using matrix inversion: 2x + 3y = 7, x - y = 1

Accepted Answer

x = 2, y = 1

Answer

x = -2, y = -1

Answer

x = 2, y = -1

Answer

x = 1, y = 2

Question 25

Which of the following is a parametric equation of the line passing through the points (1, 2) and (3, 4)?

Accepted Answer

x = 1 + 2t, y = 2 + 2t

Answer

x = 3 + t, y = 4 + 2t

Answer

x = 2 + 3t, y = 3 + 4t

Answer

x = 1 + 3t, y = 2 + 4t

Question 26

Find the slope of the line 2y + 3x = 5

Accepted Answer

-3/2

Answer

-2/3

Answer

2/3

Answer

1/2

Question 27

Identify the x-intercept of the line y = 2x - 4

Accepted Answer

2

Answer

-2

Answer

4

Answer

-4