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 @@MATH_TOKEN_13@@ and the cost of 6 hats is @@MATH_TOKEN_14@@
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 @@MATH_TOKEN_16@@ and cost of one scarf is @@MATH_TOKEN_17@@ , so from information given we can write second equation as:
@@MATH_TOKEN_18@@
We have 2 equations. Now solving for @@MATH_TOKEN_19@@ in second equation and putting that into first equation, we have:
@@MATH_TOKEN_20@@
Now,
@@MATH_TOKEN_21@@
Using distributive proper [ @@MATH_TOKEN_22@@ ] and a little algebra, we can find the value of s:
@@MATH_TOKEN_23@@
Hence, the cost of 1 scarf is $7.00
Answer choice D is right.
