Question

SOLUTIONS FOR SYSTEMS OF EQUATIONS

1. Which of the following statements would be the process that is used to describe solving a system of equation with 6 variables?

Solving a 3 order system
Solving a 6 order system
Solving a system
Solving an order system

2. Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.
2x - y = 7
2y = 4x - 14

{}
1 solution
infinite

3. Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.
x + y = 5
x + y = 7

{}
1 solution
infinite

4. Which of the following points is a solution to the system of equations shown?
y - x = -1
x + y = -5

(-3, -2)
(-6, 1)
(-2, -3)

5. Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.
x + y = 4
x - y = 0

{}
1 solution
infinite

6. Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.
3x + 2y = 6
x - y = 2

{}
1 solution
infinite

7.Which of the following points is a solution to the system of equations shown?
4x + y = 1
y = x + 6

(5, -1)
(0, 6)
(-1, 5)

8.Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.
x - y = 5
2x + y = 1

{}
1 solution
infinite

Answer 1

The person below did great but,

1) the answer is actually Solving a 6 order system

Answer 2

1. Solving an order system

2. Let us solve this one by combining the two equations:

2x – y = 7

2y = 4x – 14 --> y = 2x – 7

combine:

2x – (2x – 12) = 7

2x – 2x + 7 = 7

0 + 7 = 7

7 = 7

No variable at the end, therefore infinite solutions

3. From the given equations itself, we can see that this is impossible to have solutions, therefore:

{}

4. y – x = -1 --> y = x – 1

x + (x – 1) = -5

2x – 1 = -5

x = -2

y = x – 1 = -2 – 1 = -3

(-2, -3)

5. x = y

x + x = 4

2x = 4

x = 2 = y

(2, 2)

1 solution

6. x – y = 2 --> x = 2 + y

3 (2 + y) + 2y = 6

6 + 3y + 2y = 6

5y = 0

y = 0

x = 2 + y = 2

(0, 2)

1 solution

7. 4x + (x + 6) = 1

5x + 6 = 1

5x = -5

x = -1

y = x + 6 = -1 + 6 = 5

(-1, 5)

8. x – y = 5 --> x = 5 + y

2 (5 + y) + y = 1

10 + 2y + y = 1

3y = -9

y = -3

x = 5 + y = 5 – 3 = 2

(2, -3)

1 solution