Question

Which statements about the system are true? Check all that apply. y = 1/3 x – 4 3y – x = –7 The system has one solution. The system consists of parallel lines. Both lines have the same slope. Both lines have the same y–intercept. The equations represent the same line. The lines intersect.

Answer 1

y = 1/3 x – 4
3y – x = –7

is easier to solve if written as above, with each equation on one line.

Mult. the first eqn by -3: we get -3y = -1 - 4(-3), or -3y = 11. Add this new form of the 1st equation to the second equation:

3y – x = –7
-3y = 11
-----------------
-x = 4, or x = -4. Then y = (1/3)(-4) - 4, or y = -4/3 - 12/3 = -16/3

If this is correct, then the solution is (-4, -16/3) (one solution, and the lines intersect).

Answer 2

Same slope

Does not represent the same line

Lines do not intersect

Explanation:

We need to simplify equation and compare it to equation 1:

Equation 2

`3*y-x=-7`

We can take x to the right hand side and divided the equation by 3:

`y=(1/3)*x-7`

We can see that both lines have the slope 1/3 and thus it is true. When x=0 the lines intercept the y-axis. Lets evaluate this:

`y=(1/3)*0-4=-4`

`y=(1/3)*0-7=-7`

Therefore the lines do not have the same y-intercept

Therefore the lines do not represent the same line.

Lets see if they intersect by making y=y:

`(1/3)*x-4=(1/3)*x-7`

`-4=-7`

The lines do not intersect because there isn't a point that it intersects and -4 does not equal to -7.