In which quadrant does the solution of the system fall? y=x–1
y = –3x – 5 (1 point)
I II III IV
To determine which quadrant the solution falls in, we need to find the intersection point of the two lines.
To do this, we can set the two equations equal to each other and solve for x:
x - 1 = -3x - 5
Adding 3x to both sides gives:
4x - 1 = -5
Adding 1 to both sides:
4x = -4
Dividing both sides by 4 gives:
x = -1
Now, we can substitute this value of x back into either equation to find the corresponding y-value. Let's use the first equation:
y = -1 - 1
y = -2
Therefore, the solution to the system is (-1, -2).
From this coordinate, we can determine the quadrant by looking at the signs of x and y:
- x is negative
- y is negative
Since both x and y are negative, the solution falls in Quadrant III.
In which quadrant does the solution of the system fall? x+y=4
2x – y = 2 (1 point)
I II III IV
To determine the quadrant in which the solution of the system falls, we need to find the intersection point of the two lines.
First, let's solve the system of equations using the substitution method.
We can isolate y in the first equation:
y = 4 - x
Now, we can substitute this expression for y in the second equation:
2x - (4 - x) = 2
Simplifying, we have:
2x - 4 + x = 2
3x - 4 = 2
3x = 6
x = 2
Substituting the value of x back into the first equation to solve for y:
2 + y = 4
y = 2
Therefore, the solution to the system is (2, 2).
From this coordinate, we can determine the quadrant by looking at the signs of x and y:
- x is positive
- y is positive
Since both x and y are positive, the solution falls in Quadrant I.
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?
(1 point)
$4.00 $5.00 $6.00 $7.00
Let's assume the cost of one scarf is x dollars.
According to the given information, the cost of two hats is $1.00 more than the cost of one scarf. This can be represented as (x + $1.00) dollars.
Now, we know that the cost of four scarves is 4x dollars, and the cost of six hats is 6(x + $1.00) dollars.
We are given that the total cost of four scarves and six hats is $52.00. So, we can set up an equation:
4x + 6(x + $1.00) = $52.00
Simplifying the equation:
4x + 6x + 6 = $52.00
10x + 6 = $52.00
10x = $52 - $6
10x = $46
x = $46/10
x = $4.60
Therefore, the cost of one scarf is $4.60, which is closest to $5.00.