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

Answer:

First Question: C

Second Question: A

Third Question: D

Step-by-step 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:

$x-1=-3x-5\\x+3x=-5+1\\4x=-4\\x=\frac{-4}{4}=-1$

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:

$2(4-y)-y=2\\8-2y-y=2\\8-3y=2\\8-2=3y\\6=3y\\y=\frac{6}{3}=2$

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:

$h=\frac{s+1}{2}$

Now,

$4s+6(\frac{s+1}{2})=52$

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

$4s+\frac{6s+6}{2}=52\\\frac{8s+6s+6}{2}=52\\8s+6s+6=52*2\\8s+6s+6=104\\8s+6s=104-6\\14s=98\\s=\frac{98}{14}=7$

Hence, the cost of 1 scarf is $7.00

Answer choice D is right.