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 x value for a solution because this is a system that is graphically a pair of parallel lines. That is then classified as an inconsistent system (no solutions) as parallel lines do not intersect. One can determine that this is parallel lines because the slope is the same but with different y-intercepts. This can be shown by putting each equation into the slope-intercept form.

Answer 2

A quick, short-hand way of seeing this at a glance is to multiply both sides of equation #1 by the value "2". The "x" and "y" coefficients will be the same (6x and 2y), but the right-hand sides of the two equations will not be equal. That situation will result in the same slope for both equations but with different y-intercepts, thus giving parallel lines.

Answer 3

If that is too hard to do at a glance, then with converting both equations to slope-intercept form:

y = -3x + 1 and

y = -3x - 9/2

Looks like:

Answer 4

ok thank you for the help

Answer 5

You're welcome! Good luck in your studies and thx for the recognition! @Solmyr

Answer 6

np