Question

1. What is the solution to the system of equations?

3x - 6y = -12
x - 2y = -8
(a) Use the substitution method to justify that the given system of equations has no solution.
(b) What do you know about the two lines in this system of equations?

Answer 1

Step-by-step explanation:(a)3x - 6y = -12.,......(1)x - 2y = -8.…......(2)from equation (2),by adding 2y to both sides, x= -8 + 2y.....(3)Let's substitute the value of x in equation (1)3(-8 + 2y) - 6y = -12-24 + 6y - 6y = -126y - 6y = 12..,..(4)From equation (4) we can see that both equations (1) and (2) has no solutions for x and y(b)They are two parallel lines of slope of 2 and intercepts on y at 2 and 4

Answer 2

Explanation:

(a)

3x - 6y = -12.,......(1)

x - 2y = -8.…......(2)

from equation (2),by adding 2y to both sides, x= -8 + 2y.....(3)

Let's substitute the value of x in equation (1)

3(-8 + 2y) - 6y = -12

-24 + 6y - 6y = -12

6y - 6y = 12..,..(4)

From equation (4) we can see that both equations (1) and (2) has no solutions for x and y

(b)They are two parallel lines of slope of 2 and intercepts on y at 2 and 4