Determine the number of solutions you will have for the system 4y+x=16 and y=4-x

Question

anonymous · Answer

a graph can be made from y=4-x

mathstudent55 · Answer

The second equation is solved for y.
Can you solve the first equation for y?
What do you get?

anonymous · Answer

x=0. y=4

mathstudent55 · Answer

No asked to solve the system. The only question is how many solutions there are.

jenny.andrade · Answer

is it no solutions, impossible to determine, one solution or indefinite solutions

jdoe0001 · Answer

so   what did you get for the 2nd equation when solved for "y"?

mathstudent55 · Answer

@jenny.andrade 
Do you know how to solve the second equation for y?

anonymous · Answer

well its one set of solutions

mathstudent55 · Answer

Here is the first equation:

4y + x = 16

We want to solve it for y.
First, we subtract x from both sides:

4y = -x + 16

Now we divide both sides by 4:

$y = -\dfrac{1}{4}x + 4$

Now we bring in the first equation and we look at the system of equations with both equations solved for y.


$y = -\dfrac{1}{4}x + 4$

$y=-x + 4$

We see that the equations are different. Therefore, we have two different lines. 
We also see that the slopes are different. That means the lines intersect in one single place. That means there is exactly one solution.

jenny.andrade · Answer

Nope. I don't know anything about algebra, so its going to be one solution?

mathstudent55 · Answer

You could at least read what I wrote in response to your question.

mathstudent55 · Answer

I just spent time trying to help you, but I know how valuable your time is, so if you'd like, just read the last line of my long answer above.

anonymous · Answer

@jenny.andrade its one sol.

jenny.andrade · Answer

thank you!!!!

anonymous · Answer

:)