1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Deffense [45]
3 years ago
10

solve this system of linear equations. Separate the X- and Y- values with a comma. -9x+2y=-16 19x+3y=41​

Mathematics
2 answers:
Serjik [45]3 years ago
6 0

Answer:

(2, 1)

Step-by-step explanation:

The best way to do this to avoid tedious fractions is to use the addition method (sometimes called the elimination method).  We will work to eliminate one of the variables.  Since the y values are smaller, let's work to get rid of those.  That means we have to have a positive and a negative of the same number so they cancel each other out.  We have a 2y and a 3y.  The LCM of those numbers is 6, so we will multiply the first equation by a 3 and the second one by a 2.  BUT they have to cancel out, so one of those multipliers will have to be negative.  I made the 2 negative.  Multiplying in the 3 and the -2:

3(-9x + 2y = -16)--> -27x + 6y = -48

-2(19x + 3y = 41)--> -38x - 6y = -82

Now you can see that the 6y and the -6y cancel each other out, leaving us to do the addition of what's left:

-65x = -130 so

x = 2

Now we will go back to either one of the original equations and sub in a 2 for x to solve for y:

19(2) + 3y = 41 so

38 + 3y = 41 and

3y = 3.  Therefore,

y = 1

The solution set then is (2, 1)

olga55 [171]3 years ago
5 0

x=2 and y=1

proof:

-9x+2y=-16

-9(2)+2(1)=-16

which is a true statement

You might be interested in
(EASY QUESTION 20 POINTS)
Katen [24]
One US ton is 2000 lbs, thus 2/5 of that is just their product,

\bf \cfrac{2}{5}\cdot 2000\implies \cfrac{4000}{5}\implies 800~lbs
5 0
4 years ago
Read 2 more answers
What is the maximum height that a 24 foot ladder can safely reach if the base of the ladder should always be about 1 foot away f
Step2247 [10]

Answer: The maximum height it can safely reach is 23 feet (approximately)

Step-by-step explanation: First of all the ladder is 24 feet long. Then it needs to rest on a vertical support and it is recommended that for every 4 feet the ladder goes up, there should be a 1 foot safety distance between the base of the ladder and the vertical support. In other words, if the whole length of the ladder were to be placed on the vertical support, the 24-foot height must have a safety distance of,

Base = height/4

Base = 24/4

Base = 6

What this implies is that, as long as the whole length of the ladder (24 ft) is placed on the support, the safe distance from the base of the support would be 6 feet. At this rate, the maximum height that the ladder can reach is simply the vertical support itself. This results in a right angled triangle with hypotenuse 24 ft, and one side measuring 6ft. The unknown side can be derived by use of the Pythagoras theorem which states that,

AC^2 = AB^2 + BC^2

Where AC is the hypotenuse and AB and BC are the other two sides.

We can now substitute for the values as follows,

24^2 = 6^2 + BC^2

576 = 36 + BC^2

Subtract 36 from both sides of the equation

540 = BC^2

Add the square root sign to both sides of the equation

BC = 23.2379

By approximation, BC equals 23 feet.

That means the maximum height the ladder can SAFELY reach is 23 feet.

3 0
3 years ago
Read 2 more answers
The number of bacteria in a petri dish is 524 and growing at a rate of 7% every month. How many bacteria will there be in 7 mont
Lapatulllka [165]
A = P.e^(r.t), where P is the initial population, r = rate of growth , 
t = interval of time & e = 2.7182...

A = 524(2.7182...)^(0.07x7) = 855.33 ≈ 856

6 0
4 years ago
Jan says that a rhombus is a parallelogram and that every parallelogram is also a rhombus. Is Jan correct?
marysya [2.9K]

Answer:

No

Step-by-step explanation:

A parallelogram has opposite sides parallel and equal in length. Also, opposite angles are equal. Squares, rectangles, and rhombuses are all parallelograms. So all parallelograms are not rhombuses.

7 0
3 years ago
Pls help extra points and mark brainlist
Nezavi [6.7K]

Answer:

ABC

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • (3x + 3)(x − 5) <br><br><br> I’m confused please help me!
    15·2 answers
  • What numbers are less than -11
    15·2 answers
  • Write an equivalent expression for- <br> 3 (4+2)
    8·2 answers
  • What’s the answer for 6x + 5 = 2x -15 ?
    13·2 answers
  • The sides of ∠A are tangent to circle k(O) with radius r. Find: r, if OA=14 dm, m∠A=90°.
    15·2 answers
  • Need help! 10 points ​
    14·2 answers
  • The nth term of a sequence is 3n^2- 1
    12·1 answer
  • Someone please help me i am so bad with point slope stuff
    5·1 answer
  • Which of the following is an equivalent form of the compound inequality −44 &gt; −2x − 8 ≥ −48?
    12·1 answer
  • Write a sine function that has an amplitude of 5, a midline of 3 and a period of 6pi/7
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!