Which statements about the system are true? Check all that apply. y= -13x - 4

3y-x= -7

a
Both lines have the same y–intercept.
b
The system consists of parallel lines.
c
The equations represent the same line.
d
The system has one solution.
e
Both lines have the same slope.

D

Step-by-step explanation:

To compare the two lines, we want to a=make sure that they are in the same form.

3y-x=-7           [add both sides by x]

3y=x-7            [divide both sides by 3]

y=1/3x-7

Now that the equations are in the same form, we can compare them.

In order for the equations to have the same y-intercept, the "b" must be the same. The y-intercept for the first equation is -4, while the y-intercept for the second equation is -7. Therefore, A is not the answer.

If the lines are parallel, they must have the same slope. Parallel lines NEVER touch or cross, hence the slope has to be the same. The slope for the first equation is -13, while the slope for the second equation is 1/3. Therefore, B is not the answer.

We know that E is not the answer because the paragraph above proved that the slope are not equal.

We also know that the equations do not represent the same line. If they are the same line, the equations would be identical.

We know that D is the correct answer. A system of linear equaitons can only have ONE solution. We set the equations equal to each other to find the solution. The intersection point is the solution.

Therefore, we know that D is the right answer.

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