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

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:

Now putting    into the first equation, we get y:

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:

Now using this and substituting in Equation 2 we have:

Now using distributive property [ ] and a little algebra, we solve for y:

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

So our solution is    and  

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    and cost of one hat be  

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

Cost of 4 scarves is    and the cost of 6 hats is  

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

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

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

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

Now,

Using distributive proper [ ] and a little algebra, we can find the value of s:

Hence, the cost of 1 scarf is $7.00

Answer choice D is right.

c. side angle side. u shares the same sides