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Monica [59]
3 years ago
7

Solve this system of equations. x + y = -3 x - y = 1

Mathematics
2 answers:
Ksju [112]3 years ago
7 0
The correct answer is A.
Sindrei [870]3 years ago
4 0
A. (-1,-2)

Because:
x + y = -3                                     
-1 + (-2) = -3
-3 = -3

x - y = 1
-1 - (-2) = 1
-1 + 2 = 1
1 = 1
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Amanda went to the store to purchase ink pens. She found three kinds of pens. The first cost $4 each; the price of the second ki
KonstantinChe [14]

Answer:

Amanda buy first kind of pen = 3

Amanda buy second kind of pen = 2

Amanda buy third kind of pen = 15

Step-by-step explanation:

Given - Amanda went to the store to purchase ink pens. She found three    

            kinds of pens. The first cost $4 each; the price of the second kind

            was 4 for $1; and the cost for the third kind was 2 for $1. She bought

            20 pens and she bought at least one of each kind. (It is possible to

            buy only 1 of the pens that are "4 for $1" or "2 for $1".) The cost was

            $20.

To find - When she got back to her office, Amanda decided to turn this into

              a math problem for me. She asked: how many of each kind did I

              buy?

Proof -

Let Amanda buy first kind of pen = x

                      second kind of pen = y

                           third kind of pen = z

As given,

She bought total pen = 20

⇒x + y + z = 20          ...............(1)

Now,

As given,

cost for first kind pen = $4 for 1 pen

As she bought x pens of first kind , so

Cost of x pens of first kind = $4x

Now,

The price of the second kind was 4 for $1

⇒Cost of second kind = $\frac{1}{4} for 1 pen

As she bought y pens of send kind , so

Cost of y pens of second kind = $\frac{1}{4}y

Now,

The price of the third kind was 2 for $1

⇒Cost of third kind = $\frac{1}{2} for 1 pen

As she bought z pens of send kind , so

Cost of z pens of third kind = $\frac{1}{2}z

Now,

As given, The cost was $20

⇒4x + \frac{1}{4}y + \frac{1}{2}z = 20

⇒16x + y + 2z = 80             .....................(2)

∴ we get 2 equations

x + y + z = 20                   .....................(1)

16x + y + 2z = 80             .....................(2)

Now,

Subtract equation (1) from equation (2) , we get

16x + y + 2z  - ( x+ y + z )= 80 - 20

⇒16x + y + 2z - x - y - z = 60

⇒15x + z = 60

⇒z = 60 - 15x

Now,

Put the value of z in equation (1) , we get

x + y + 60 - 15 x = 20

⇒ y - 14x = 20 - 60

⇒y - 14x = -40

⇒14x - y = 40

⇒y = 14x - 40

Now,

we get

z = 60 - 15x

y = 14x - 40

As given

she bought at least one of each kind

it means x > 1, y > 1, z > 1

Now,

If x = 1, then y = 14 - 40 = -26

Not possible

If x = 2 , then y = 14(2) - 40 = -12

Not possible

If x = 3, then y = 14(3) - 40 = 2 and z = 60 - 15(3) = 15

Possible.

If x = 4,  then y = 14(4) - 40 = 16 and z = 60 - 15(4) = 0

Not Possible.

If x = 5, then y = 14(5) - 40 = 30 and z = 60 - 15(5) = -15

Not Possible.

∴ we get

x = 3, y = 2, z = 15

Amanda buy first kind of pen = x = 3

Amanda buy second kind of pen = y = 2

Amanda buy third kind of pen = z = 15

7 0
2 years ago
Can anyone help me with the problem in the picture?
torisob [31]
X = 45.

Since opposite exterior angles are congruent, you can set the 2 values equal to each other. When you solve for x, you should get 45.
3 0
2 years ago
Please help I am struggling. Caled draws two triangles and claims that the triangles are congruent. For the case where his claim
krok68 [10]

Answer:

Everything except the last one about rigid transformations. Rigid transformations change the shape in size or the shape completely.

7 0
2 years ago
A lake near the Arctic Circle is covered by a 2-meter-thick sheet of ice during the cold winter months. When spring arrives, the
Kaylis [27]

Answer:

The answer would be y-intercept and a point that is NOT an intercept

Step-by-step explanation:

To describe a point on the graph, we need a corresponding  

(x,y)(x,y)

(x,y)

left parenthesis, x, comma, y, right parenthesis

pair.

In our case, these are corresponding values of weeks since spring arrives and thickness of ice.

weeks since spring arrivedthickness of ice↓↓(x,y)\begin{aligned} \scriptsize\text{weeks since spring arrived}&\quad\scriptsize\text{thickness of ice} \\ \downarrow&\quad\downarrow \\ \large (x &,\quad\large y) \end{aligned}

weeks since spring arrived

↓

(x

​

thickness of ice

↓

,y)

​

To describe the slope of the graph, we need information about the rate of change of the relationship.

In our case, this is the rate at which the thickness of ice changes over time (in meters per week).

Hint #2

2 / 4

The ice is  

22

2

2

meters thick at the start of spring, when  

00

0

0

weeks have passed. This corresponds to the point  

(0,2)(0,2)

(0,2)

left parenthesis, 0, comma, 2, right parenthesis

and is a  

yy

y

y

-intercept.

Hint #3

3 / 4

After  

33

3

3

weeks, the sheet is only  

1.251.25

1.25

1, point, 25

meters thick. This corresponds to the point  

(3,1.25)(3,1.25)

(3,1.25)

left parenthesis, 3, comma, 1, point, 25, right parenthesis

and is not an intercept.

Hint #4

4 / 4

The  

yy

y

y

-intercept and a point that is not an intercept is given

7 0
3 years ago
Students in Mrs. Palmer's third grade class are working on times tables, and they demonstrate mastery by passing tests. Evan has
hammer [34]

Answer: Don't know

Step-by-step explanation:

4 0
2 years ago
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