Ask question

Ask question

All categories

3 years ago

11

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 4x -

5y = 24 2x + 3y = -10 one and only one solution infinitely many solutions no solution Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.)

1 answer:

zepelin [54]3 years ago

3 0

Answer:it has one and only one solution.

Step-by-step explanation:

The given system of equations is expressed as

4x - 5y = 24 - - - - - - - - - - - - -1

2x + 3y = -10 - - - - - - - - - - - - - 2

We would eliminate x by multiplying equation 1 by 1 and equation 2 by 2. It becomes

4x - 5y = 24

4x + 6y = - 20

Subtracting, it becomes

- 11y = 44

Dividing the left hand side and the right hand side of the equation by

- 11, it becomes

- 11y/- 11 = 44/- 11

y = - 4

Substituting y = - 4 into equation 2, it becomes

2x + 3 × - 4 = -10

2x - 12 = - 10

2x = - 10 + 12

2x = 2

Dividing the left hand side and the right hand side of the equation by

2, it becomes

2x/2 = 2/2

x = 1

You might be interested in

StartFraction one-half left-parenthesis x plus 12 right-parenthesis equals 4 x minus 1.(x + 12) = 4x – 1

Alika [10]

Answer:

1/2.(x+12)=4x-1

x+12=2(4x-1)

x+12=8x-2

Group like terms

12+2=8x-x

14=7x

Divide both sides by 7

x=2

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

The cost C (in dollars) of making n watches is represented by C = 15n + 85 .

AURORKA [14]

So the answer should be 48.58 if not then it could be 278n

5 0

3 years ago

What is the locus of all points that are a fixed distance from a given point? A) angle B) circle C) triangle D) line segment

GaryK [48]

A circle is a fixed distance from all other points on the circle

5 0

3 years ago

Given: circle k(O), m∠P=95°, m∠J=110°, m∠LK=125°<br> Find: m∠PJ

IRINA_888 [86]

Answer:

The measure of the arc PJ is $75\°$

Step-by-step explanation:

step 1

Find the measure of angle L

we know that

In a inscribed quadrilateral opposite angles are supplementary

so

$m$

we have

$m$

substitute

$m$

$m$

step 2

Find the measure of arc KJ

we know that

The inscribed angle measures half that of the arc comprising

so

$m$

substitute the values

$95\°=\frac{1}{2}(125\°+arc\ KJ)$

$190\°=(125\°+arc\ KJ)$

$arc\ KJ=190\°-125\°=65\°$

step 3

Find the measure of arc PJ

we know that

The inscribed angle measures half that of the arc comprising

so

$m$

substitute the values

$70\°=\frac{1}{2}(65\°+arc\ PJ)$

$140\°=(65\°+arc\ PJ)$

$arc\ PJ=140\°-65\°=75\°$

5 0

2 years ago

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Use the circle graph sh

mel-nik [20]

Answer: 500 people

Step-by-step explanation:

Let there are x people in the survey.

According to the question,

People who like football as their favorite sports = 42 % of x = 0.42 x

People who like baseball as their favorite sports = 33 % of x = 0.33 x

People who like soccer as their favorite sports = 25 % of x = 0.25 x

But, 210 people said football was their favorite sport.

⇒ 0.42 x = 210

⇒ 42 x = 21000

⇒ x = 500

Therefore, there are 500 people in the survey.

4 0

3 years ago

Read 2 more answers