Question

Is the following system consistent or inconsistent?

2y = x - 7

-2x - 6y = -14
A. Consistent
B. Inconsistent

Answer 1

Thanks

Answer 2

if the equations have no solution, then they are inconsistent. If the equations have one or more solutions, then they are consistent.

2y = x - 7
x = 2y + 7

-2x - 6y = -14
-2(2y + 7) - 6y = -14
-4y - 14 - 6y = -14
-4y - 6y = -14 + 14
-10y = 0
y = 0

2y = x - 7
2(0) = x - 7
0 = x - 7
x = 7

check..
-2x - 6y = -14
-2(7) - 6(0) = -14
-14 - 0 = -14
-14 = -14 (correct)

The solution to this system of equations is (7,0)
And since it has one solution, then it is consistent

Answer 3

or you could have done this...
put both equations in y = mx + b form

2y = x - 7
y = 1/2x - 7/2
slope is 1/2 and y intercept is -7/2

-2x - 6y = -14
-6y = 2x - 14
y = -1/3x + 7/3
slope is -1/3 and y intercept is 7/3

Now remember this...
if they have same slopes, but different y intercepts, they are parallel lines and do not intersect. They have no solutions.
if they have same slopes and same y intercepts, they are same line and have infinite solutions.
If they have different slopes and different y intercepts, they will have 1 solution and be consistent