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
damaskus [11]
3 years ago
14

find the value of a and b for which the system of equations has infinitely many solutions : 2x + 3y = 7 ; (a-b)x + (a+b)y = 3a +

b - 2​
Mathematics
1 answer:
hodyreva [135]3 years ago
8 0

Answer:

a= 5    and   b=1

Step-by-step explanation:

To solve, we will follow the steps below:

2x + 3y = 7

(a-b)x + (a+b)y = 3a + b - 2​

We should note that since it has infinitely many solutions then,

\frac{a_{1} }{a_{2} }   =  \frac{b_{1} }{b_{2} }  = \frac{c_{1} }{c_{2} }

Hence

2/a-b  =  3/a+b   =     7/3a +b-2

2/a-b  =  3/a+b

cross-multiply

3(a-b) = 2( a+b)

open the bracket

3a - 3b = 2a + 2b

collect like term

3a - 2a = 2b + 3b

a = 5b  -------------------------------------------(1)

Similarly

3/a+b   =     7/3a +b-2

cross-multiply

7(a+b)  = 3(3a+b -2)

7a + 7b = 9a + 3b -6

take all the variables to the left-hand side of the equation

7a - 9a+ 7b-3b =   -6

-2a + 4b = -6 ---------------------------------(2)

but a = 5b

substitute a= 5b in equation (2)   and solve for b

-2(5) + 4b = -6

-10  +  4b  = -6

add 10 to both-side of the equation

-10  + 10+ 4b  = -6+10

4b = 4

divide both-side of the equation by 4

b = 1

substitute b= 1 in equation (1)

a = 5b

a =5(1)

a=5

Therefore,   a= 5    and   b=1

You might be interested in
The length of the hypotenuse of a right triangle is 14 inches. If the length of one leg is 6 inches, what is the approximate len
Mice21 [21]
In this question, you need to use Pythagoras' Theorem, c^2 - b^2 = a^2. In this case, C is 14 and B is 6, so you would do 14^2 - 6^2 = 196 - 36 = 160, and the approximate square root of 160 is 12.6 inches, which is your answer.

I hope this helps!
8 0
3 years ago
Read 2 more answers
Every hour at work, you are able to ship out the same number of
never [62]

Answer:

its 6

Step-by-step explanation:

divided 12 with 2 and divided 30 with 5

8 0
3 years ago
What is the atomic number of an atom?
mariarad [96]

Answer:

The number of protons

Step-by-step explanation:

Its the correct answer

6 0
3 years ago
Asia uses an overhead projector to enlarge a drawing. The original measure 75 cm wide by 100 cm high. She moves the projector so
Scorpion4ik [409]
The ratio of the width to the height is 3:4.
So, just multiply the width by 4/3, which gives you <span>500cm.</span>
3 0
3 years ago
What does the expression 12f<br> =24 represent?
Law Incorporation [45]
You have to divide both sides by 12 so 12f/12 =24/12 is f = 2
6 0
3 years ago
Read 2 more answers
Other questions:
  • There are 8 rows of chairs in the auditorium. Three of the rows are empty. What fraction of the rows are empty?
    11·1 answer
  • Don bought his car for $20,350. It is expected to depreciate an average of 11% each year during the first 5 years.
    10·2 answers
  • What is the simplified expression for 3 a squared + 9 a b + 5 minus 4 a squared minus 4 a b + 3?
    5·2 answers
  • Jasper has 7 more checkers left than Karen does.Jaspar has 9 checkers left. write and solve an addition equation to find out how
    12·2 answers
  • The standard normal distribution has a mean of<br><br> and a standard deviation of
    14·1 answer
  • D(n) = 6 - 4(n - 1)d(n)=6−4(n−1)
    7·1 answer
  • !HELP! What is the equation for the following absolute-value functions?
    8·1 answer
  • 3 (2x - 5) + 20 + 5x i need help
    10·1 answer
  • Select the correct answer.
    8·2 answers
  • Please help!!!!!!!!!!
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!