Question

In which quadrant does the solution of the system fall?

y=x-1
y=-3x-5
a. 1
b. 2
c. 3
d. 4
In which quadrant does the solution of the system fall?
x+y=4
2x-y=2
a. 1
b. 2
c. 3
d. 4
The cost of four scarves and six hats is $52.00. The cost of two hats is $1.00 more than the cost of one scarf. What is the cost of one scarf?
a. $4.00
b. $5.00
c. $6.00
d. $7.00

Answer 1

did you figure out the answers i need help!!!!!!!!!!!!!!!!!!!!!!!!

Answer 2

First Question: C

Second Question: A

Third Question: D

Explanation:

First Question:

We need to solve the equation first and see the x and y point of the solution.

We can substitute Equation 1 into Equation 2 given, and then solve for x:

`x-1=-3x-5\\x+3x=-5+1\\4x=-4\\x=(-4)/(4)=-1`

Now putting
`x=-1` into the first equation, we get y:

`y=(-1)-1\\y=-2`

Hence, the solution is x = -1 and y = -2

Both x and y negative falls in the 3rd quadrant.

Answer choice C is right.

Second Question:

Let's solve the equation using substitution method and find the solution first.

Solving for x in Equation 1 gives us:

`x=4-y`

Now using this and substituting in Equation 2 we have:

`2(4-y)-y=2`

Now using distributive property [
`a(b+c)=ab+ac` ] and a little algebra, we solve for y:

`2(4-y)-y=2\\8-2y-y=2\\8-3y=2\\8-2=3y\\6=3y\\y=(6)/(3)=2`

Now using value of
`y=2` and putting it in the First Equation and rearranging gives us the value of x:

`x+(2)=4\\x=4-2\\x=2`

So our solution is
`x=2` and
`y=2`

Both x and y are positive and they fall in 1st quadrant.

Choice A is right.

Third Question:

We let cost of one scarf be
`s` and cost of one hat be
`h`

"The cost of four scarves and six hats is $52.00":

Cost of 4 scarves is
`4s` and the cost of 6 hats is
`6h`

The total cost is $52, hence we can write our first equation:

`4s+6h=52`

"The cost of two hats is $1.00 more than the cost of one scarf":

Cost of 2 hats is
`2h` and cost of one scarf is
`s` , so from information given we can write second equation as:

`2h=s+1`

We have 2 equations. Now solving for
`h` in second equation and putting that into first equation, we have:

`h=(s+1)/(2)`

Now,

`4s+6((s+1)/(2))=52`

Using distributive proper [
`a(b+c)=ab+ac` ] and a little algebra, we can find the value of s:

`4s+(6s+6)/(2)=52\\(8s+6s+6)/(2)=52\\8s+6s+6=52*2\\8s+6s+6=104\\8s+6s=104-6\\14s=98\\s=(98)/(14)=7`

Hence, the cost of 1 scarf is $7.00

Answer choice D is right.