Solving Equations Using Inverse Matrices Quiz

1. Solve this equation given below x+y+z = -1 2x+ y = 2 -3x = -9

𝑥 = -3, 𝑦 = −4, 𝑧 = 0

𝑥 = 3, 𝑦 = 4, 𝑧 = 0

𝑥 = 2, 𝑦 = −4, 𝑧 = 0

𝑥 = 3, 𝑦 = −4, 𝑧 = 0

The given set of equations can be solved using substitution or elimination method. By substituting the value of x from the third equation into the second equation, we get y = -4. Substituting the values of x and y into the first equation, we get z = 0. Therefore, the solution to the equation is x = 3, y = -4, and z = 0.

Explanation

The given set of equations can be solved using substitution or elimination method. By substituting the value of x from the third equation into the second equation, we get y = -4. Substituting the values of x and y into the first equation, we get z = 0. Therefore, the solution to the equation is x = 3, y = -4, and z = 0.

2. Solve this equation given below x-2y+z= -9 2y+3z= 16 4y=8

𝑥 = 9, 𝑦 = 2, 𝑧 = - 4

𝑥 = −9, 𝑦 = -2, 𝑧 = 4

𝑥 = −9, 𝑦 = 2, 𝑧 = 4

𝑥 = −9, 𝑦 = - 2, 𝑧 = - 4

The given system of equations can be solved using the method of substitution. From the third equation, we can solve for y: y = 2. Substituting this value of y into the second equation, we can solve for z: 2(2) + 3z = 16, which gives z = 4. Substituting the values of y = 2 and z = 4 into the first equation, we can solve for x: x - 2(2) + 4 = -9, which gives x = -9. Therefore, the correct answer is 𝑥 = -9, 𝑦 = 2, 𝑧 = 4.

Explanation

The given system of equations can be solved using the method of substitution. From the third equation, we can solve for y: y = 2. Substituting this value of y into the second equation, we can solve for z: 2(2) + 3z = 16, which gives z = 4. Substituting the values of y = 2 and z = 4 into the first equation, we can solve for x: x - 2(2) + 4 = -9, which gives x = -9. Therefore, the correct answer is 𝑥 = -9, 𝑦 = 2, 𝑧 = 4.

3. Solve this equation given below x+y=4 2x+3y=9

𝑥 = -3, 𝑦 = -1

𝑥 = 3, 𝑦 = -1

𝑥 = 3, 𝑦 = 1

𝑥 = -3, 𝑦 = 1

The correct answer is 𝑥 = 3, 𝑦 = 1 because when we substitute these values into the given equations, we get a true statement. When we substitute 𝑥 = 3 and 𝑦 = 1 into the first equation, we get 3 + 1 = 4, which is true. When we substitute 𝑥 = 3 and 𝑦 = 1 into the second equation, we get 2(3) + 3(1) = 9, which is also true. Therefore, 𝑥 = 3 and 𝑦 = 1 satisfy both equations and are the correct solution to the given system of equations.

Explanation

The correct answer is 𝑥 = 3, 𝑦 = 1 because when we substitute these values into the given equations, we get a true statement. When we substitute 𝑥 = 3 and 𝑦 = 1 into the first equation, we get 3 + 1 = 4, which is true. When we substitute 𝑥 = 3 and 𝑦 = 1 into the second equation, we get 2(3) + 3(1) = 9, which is also true. Therefore, 𝑥 = 3 and 𝑦 = 1 satisfy both equations and are the correct solution to the given system of equations.

4. Solve this equation? 2x+4y-z= -3 y+z= 4 2y=-2

𝑥 = -3, 𝑦 = −1, 𝑧 = -5

𝑥 = -3, 𝑦 = −1, 𝑧 = 5

𝑥 = 3, 𝑦 = −1, 𝑧 = 5

𝑥 = 3, 𝑦 = −1, 𝑧 = -5

The given system of equations can be solved by substitution or elimination method. By substituting the value of y from the second equation into the first equation, we get 2x + 4(4 - z) - z = -3. Simplifying this equation gives 2x - 3z = -19. By substituting the value of y from the third equation into the second equation, we get -2 + z = 4, which gives z = 6. Substituting the value of z into the first equation, we get 2x + 4(4 - 6) - 6 = -3, which simplifies to 2x - 14 = -3. Solving this equation gives x = 3. Therefore, the correct answer is 𝑥 = 3, 𝑦 = -1, 𝑧 = 5.

Explanation

The given system of equations can be solved by substitution or elimination method. By substituting the value of y from the second equation into the first equation, we get 2x + 4(4 - z) - z = -3. Simplifying this equation gives 2x - 3z = -19. By substituting the value of y from the third equation into the second equation, we get -2 + z = 4, which gives z = 6. Substituting the value of z into the first equation, we get 2x + 4(4 - 6) - 6 = -3, which simplifies to 2x - 14 = -3. Solving this equation gives x = 3. Therefore, the correct answer is 𝑥 = 3, 𝑦 = -1, 𝑧 = 5.

5. Solve this equation given below 2x+3y =-4 3x- y = 5

𝑥 = -1, 𝑦 = 2

𝑥 = 1, 𝑦 = 2

𝑥 = 1, 𝑦 = −2

𝑥 = -1, 𝑦 = −2

The correct answer is 𝑥 = 1, 𝑦 = -2. This can be determined by solving the given system of equations using the method of substitution or elimination. By substituting the value of 𝑥 = 1 into the second equation, we get 3(1) - 𝑦 = 5, which simplifies to -𝑦 = 2. Solving for 𝑦, we find 𝑦 = -2. Substituting this value of 𝑦 back into the first equation, we get 2(1) + 3(-2) = -4, which simplifies to -4 = -4. Therefore, the solution to the system of equations is 𝑥 = 1, 𝑦 = -2.

Explanation

The correct answer is 𝑥 = 1, 𝑦 = -2. This can be determined by solving the given system of equations using the method of substitution or elimination. By substituting the value of 𝑥 = 1 into the second equation, we get 3(1) - 𝑦 = 5, which simplifies to -𝑦 = 2. Solving for 𝑦, we find 𝑦 = -2. Substituting this value of 𝑦 back into the first equation, we get 2(1) + 3(-2) = -4, which simplifies to -4 = -4. Therefore, the solution to the system of equations is 𝑥 = 1, 𝑦 = -2.

6. Solve this equation given below 2x+3y =7 3x- 4y = 2

𝑥 = -2, 𝑦 = -1

𝑥 = -2, 𝑦 = 1

𝑥 = 2, 𝑦 = -1

𝑥 = 2, 𝑦 = 1

The correct answer is 𝑥 = 2, 𝑦 = 1. This means that when we substitute 𝑥 = 2 and 𝑦 = 1 into the given equations, both equations will be satisfied. Therefore, this solution pair is the correct solution to the given system of equations.

Explanation

The correct answer is 𝑥 = 2, 𝑦 = 1. This means that when we substitute 𝑥 = 2 and 𝑦 = 1 into the given equations, both equations will be satisfied. Therefore, this solution pair is the correct solution to the given system of equations.

7. Solve this equation given below 3x+y=0 x-6y=38

𝑥 = -2, 𝑦 = −6

𝑥 = 2, 𝑦 = −6

𝑥 = 2, 𝑦 = 6

𝑥 = 2, 𝑦 = −4

The given equations are a system of linear equations. By solving the system, we find that the values of x and y that satisfy both equations are x = 2 and y = -6. Therefore, the answer is x = 2, y = -6.

Explanation

The given equations are a system of linear equations. By solving the system, we find that the values of x and y that satisfy both equations are x = 2 and y = -6. Therefore, the answer is x = 2, y = -6.

8. Solve this equation given below x+y+z = -1 2x-y+z = 19 3x- 2y- 4z = 16

𝑥 = 4, 𝑦 = −8, 𝑧 = -3

𝑥 = -4, 𝑦 = −8, 𝑧 = 3

𝑥 = -4, 𝑦 = −8, 𝑧 = -3

𝑥 = 4, 𝑦 = −8, 𝑧 = 3

The given system of equations can be solved using the method of substitution or elimination. By solving the equations, it is found that the values of x, y, and z that satisfy all three equations are x = 4, y = -8, and z = 3. Therefore, the answer 𝑥 = 4, 𝑦 = -8, 𝑧 = 3 is correct.

Explanation

The given system of equations can be solved using the method of substitution or elimination. By solving the equations, it is found that the values of x, y, and z that satisfy all three equations are x = 4, y = -8, and z = 3. Therefore, the answer 𝑥 = 4, 𝑦 = -8, 𝑧 = 3 is correct.

9. Solve this equation given below 3x-4y= 0 3x+2y =36

𝑥 = -8, 𝑦 = -6

𝑥 = 8, 𝑦 = -6

𝑥 = 8, 𝑦 = 6

𝑥 = -8, 𝑦 = 6

The correct answer is 𝑥 = 8, 𝑦 = 6. This is the correct answer because when we substitute these values into the given equations, we get 3(8) - 4(6) = 0 and 3(8) + 2(6) = 36, which satisfies both equations.

Explanation

The correct answer is 𝑥 = 8, 𝑦 = 6. This is the correct answer because when we substitute these values into the given equations, we get 3(8) - 4(6) = 0 and 3(8) + 2(6) = 36, which satisfies both equations.

10. Solve this equation given below 2x-y+4z= 7 x-3y+z= -2 3x- 2y + 2z = -2

𝑥 = −2, 𝑦 = -1, 𝑧 = -3

𝑥 = −2, 𝑦 = -1, 𝑧 = 3

𝑥 = −2, 𝑦 = 1, 𝑧 = 3

𝑥 = −2, 𝑦 = 1, 𝑧 = -3

The given equation is a system of linear equations with three variables (x, y, and z). To solve the system, we can use the method of elimination or substitution. By performing the necessary operations, we find that the values x = -2, y = 1, and z = 3 satisfy all three equations. Therefore, the given answer 𝑥 = −2, 𝑦 = 1, 𝑧 = 3 is correct.

Explanation

The given equation is a system of linear equations with three variables (x, y, and z). To solve the system, we can use the method of elimination or substitution. By performing the necessary operations, we find that the values x = -2, y = 1, and z = 3 satisfy all three equations. Therefore, the given answer 𝑥 = −2, 𝑦 = 1, 𝑧 = 3 is correct.