Question

The system, 6x - 4y = 5 and 9x - 6y = 5, is consistent.
True
False

Answer 1

6x - 4y = 5 --> (3)6x - 4y = 5
9x - 6y = 5 -->(-2)9x - 6y = 5
----------
12x - 12y = 15 (result of multiplying by 3)
-18x + 12y = -10 (result of multiplying by -2)
----------add
-6x = 5
x = - 5/6

now sub - 5/6 in for x into either of the original equations
9x - 6y = 5
9(-5/6) - 6y = 5
-45/6 - 6y = 5
-45/6 - 5 = 6y
-45/6 - 30/6 = 6y
-75/6 = 6y
(-75/6)/6 = y
-75/6 x 1/6 = y
- 75/36 = y
- 25/13 = y

check..
6x - 4y = 5
6(-5/6) - 4(-25/13) = 5
-5 + 100/13 = 5
- 65/13 + 100/13 = 5
35/13 = 5
2 9/13 = 5 (incorrect)

False. The system of equations is not consistent.
An equation is consistent if it has a solution. If it does not have a solution, it is not consistent.