Question

What is the value of the x variable in the solution to the following system of equations?

3x + y = 1
6x + 2y = −9

0

2

There is no x value as there is no solution to this system

x can be any value as there are infinitely many solutions to this system

Answer 1

There is no solution
(if you consider the graphs of these lines they will never intersect since they are parallel)

Answer 2

notice that if you divide the 2nd equation by 2 (both sides of the = sign, all terms) you get
3x + y = -9/2

your 2 equations are now
3x + y = 1
3x + y = -9/2

a "solution" is an (x,y) pair that works in both equations. Say we find an (x,y) pair that "works" for the 1st equation. (in other words 3x+y will be 1)
then in the 2nd equation, we know 3x+y is 1, and we get 1= -9/2
which is not true. This tells us there is no solution, no (x,y) pair that works for both equations.

Answer 3

Or using BAdhi's idea

change both equations to slope-intercept form
3x + y = 1 ---> y = -3x+1
6x + 2y = −9 --> y = -3x -9/2

these lines have the same slope, but different y intercepts. They are parallel lines and never intersect. that means there is no (x,y) pair that sits on both lines. (which is what would happen if the lines intersected). So, no solution

Answer 4

ok thank you for the help