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Grace [21]
3 years ago
8

How many solutions does this system have? y = 3 x minus 5. y = negative x + 4. one two an infinite number no solution

Mathematics
2 answers:
____ [38]3 years ago
8 0

Answer:

Step-by-step explanation:

6

mote1985 [20]3 years ago
6 0

Answer:

One

Step-by-step explanation:

y = 3 x - 5.

y = -x + 4.

x=9/4 and y=7/4

1 solution (9/4 , 7/4)

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Jane’s buying clothes. She can get 5 shirts & 4 sweaters for $229 or she can get 2 shirts & 3 sweaters for $128. How muc
makkiz [27]

Cost of 1 shirt is \$25 and cost of one sweater is \$26

<u>Solution: </u>

Given that  Jane’s buying clothes.

She can get 5 shirts & 4 sweaters for \$229

She can get 2 shirts & 3 sweaters for \$128

Need to determine cost of 1 shirt and 1 sweater.

Let assume cost of 1 shirt = \$x

And assume cost of 1 sweater = \$y

Let us create equations from give conditions

First condition is Cost of 5 shirt + cost of 4 sweater = \$229

\begin{array}{l}{\text { cost of 5 shirts }=5 \times \text { cost of 1 shirt }=5 \times x=5 x} \\\\ {\text { cost of 4 sweater }=4 \times \text { cost of 1 sweater }=4 \times y=4 y}\end{array}

So using first condition equation which we get is as follows

5 x+4 y=229 \rightarrow (1)

Second condition is Cost of 5 shirt + cost of 4 sweater = \$128

\begin{array}{c}{\text { cost of } 2 \text { shirts }=2 \times \text { cost of } 1 \text { shirt }=2 \times x=2 x} \\\\ {\text { cost of } 3 \text { sweater }=3 \times \text { cost of } 1 \text { sweater }=3 \times y=3 y}\end{array}

So using second condition equation which we get is as follows

2 \mathrm{x}+3 \mathrm{y}=128\quad\rightarrow (2)

Now we have two equations to be solved

\begin{array}{l}{5 x+4 y=229 \rightarrow (1)} \\\\ {2 x+3 y=128 \rightarrow (2)}\end{array}

On multiplying equation (1) by 2 and equation (2) by 5 to make coefficients of x equal in both equations, we get

\begin{array}{l}{2 x(5 x+4 y)=2\times 229} \\\\ {10 x+8 y=458 \rightarrow (3)} \\\\ {5 x(2 x+3 y)=5 \times 128} \\\\ {10 x+15 y=640 \rightarrow (4)}\end{array}

On subtracting (3) from (4), we get

\begin{array}{l}{(10 \mathrm{x}-10 \mathrm{x})+(15 \mathrm{y}-8 \mathrm{y})=640-458} \\\\ {\Rightarrow 7 \mathrm{y}=182} \\\\ {\Rightarrow \mathrm{y}=\frac{182}{7}=26}\end{array}

On substituting y = 26 in equation (1) we get

\begin{array}{l}{\Rightarrow 5 \mathrm{x}+(4 \times 26)=229} \\\\ {\Rightarrow 5 \mathrm{x}=229-104} \\\\ {\Rightarrow 5 \mathrm{x}=125} \\\\ {\Rightarrow \mathrm{x}=\frac{125}{5}=25}\end{array}

Cost of 1 shirt = \$x = \$25

Cost of 1 sweater = \$y = \$26  

7 0
3 years ago
Consider the parametric equations below.
maksim [4K]

Solve the second equation for t, then substitute it into the first equation.

y = t + 2 \implies t = y-2

x = t^2 - 3 \implies \boxed{x = (y-2)^2 - 3}

3 0
1 year ago
You are flying from Denver to Albuquerque. The distance is 349 miles between airports and takes 1 hour and 20 minutes to travel
kogti [31]

Answer:

  • car trip is faster than plane trip

Step-by-step explanation:

The less time the trip takes the faster the trip is.

<u>1. Plane</u>: build a table with the given times for flying and sum up every stage of the flying trip:

Stage                                                 time

  • On air                                       1 h: 20'
  • Check in and get seated        2 h
  • To take off                                1 h
  • Disembark                                1 h
  • Get a rental car                        1 h

                                                        ______

                                      Sum            6 h: 20'

<u>2. Car</u>.

  • Given total time: 6 h

<u>3. Comparisson</u>: 6 h < 6 h : 20' ⇒ car trip is faster than plane trip

4 0
3 years ago
What are the factors of x2 – x – 6? Check all that apply.
Zina [86]
The factors would be (x-3)(x+2)
5 0
2 years ago
There are 16 people at a party. They want to set up relay teams with 3 exactly people each. Can they do it? Explain.
olga_2 [115]
No, since 16 is not divisible by 3, there will be 1 extra perosn
4 0
4 years ago
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