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
Aneli [31]
2 years ago
15

Use the method of elimination to solve the pair of simultaneous equation 3a=2b+1,3b=5a-3​

Mathematics
2 answers:
BARSIC [14]2 years ago
7 0

Answer:

       a = 3

        b = 4

Step-by-step explanation:

Simultaneous equation

              3a = 2b + 1

         3a - 2b = 1  ------------------(I)

               3b  = 5a - 3

       -5a + 3b = -3 --------------(II)

Multiply equation (I) by 3  & equation (II) by  2 and then add. So, now 'b' will be eliminated and we can find the value of 'a'.

(I)*3       9a - 6b = 3

(II)*2    <u>-10a + 6b = -6</u>  {Now add}

            -a            = -3

                       a = -3/(-1)

        \sf \boxed{a  = 3}

Plugin a = 3 in equation (I)

              3*3 - 2b = 1

                  9 - 2b = 1

                     -2b  = 1 - 9   {Subtracting 9 from both sides}

                      -2b = - 8        

                         b = (-8)/(-2)         {Dividing both sides by (-2_}

          \sf \boxed{b = 4}                      

IgorLugansk [536]2 years ago
5 0

Answer:

  (a, b) = (3, 4)

Step-by-step explanation:

In order to eliminate one of the variables in this system of equations, both equations need to be multiplied by different numbers before they are added or subtracted. We can eliminate the 'b' variable by subtracting 3 times the first equation from 2 times the second. (Putting the 'b' terms on the same side of the equal sign makes this easier.)

__

  2(3b) -3(2b +1) = 2(5a -3) -3(3a)

  6b -6b -3 = 10a -6 -9a

  3 = a . . . . . . . add 6 and collect terms

  3b = 5(3) -3 . . . . use the second equation to find b from a

  b = 4 . . . . . . . divide by 3

The solution is (a, b) = (3, 4).

_____

The multiplier used in each case is the coefficient of the variable in the other equation. The two equations have 'b' coefficients of 2 and 3, so we multiplied the equations by 3 and 2 before subtracting. That makes the 6b terms cancel, leaving only terms with the 'a' variable.

By swapping sides of the equation the way we did, the 'a' terms end up on the same side of the equal sign, which is where we want them. Likewise, the 'b' terms end up on the same side of the equal sign, so their cancellation is easier to see.

You might be interested in
Which algebraic expression is represented by the model?
bogdanovich [222]

Answer:

Contributing

Step-by-step explanation:

Just contribute the number that is not is the column to the number that is in the column

6 0
2 years ago
630<br> Solve for &lt;2.<br> *2 = [?]°<br> 142<br> 57°123°<br> please explain as well
AlexFokin [52]

Step-by-step explanation:

the total angles in the triangle are 180°

so,

63° + 57° + ∠2 = 180°

120° + ∠2 = 180°

∠2 = 180° - 120°

∠2 = 60°

<h3>#CMIIW</h3>

7 0
2 years ago
Answer all three questions
inn [45]

Answer:

3 . al of this

4 . keeping in heat

3 0
2 years ago
What has a domain of x &gt; -3
tresset_1 [31]
Wooo nada I just want ya to be a good friend to
7 0
3 years ago
X 2.2.PS-15
Sergio [31]

Answer:

In 6/ 12 hours they will be the same.

4 0
2 years ago
Other questions:
  • A train travels at a constant speed of 35mi/h.<br> How long does it take the train to travel 490 mi?
    10·1 answer
  • 28,-(-73),(-65),(95),-(47) least to greatest
    12·2 answers
  • Type the missing number in this sequence:<br>1,<br>2,<br>4,<br>16​
    12·2 answers
  • 8(5g+5−2) = plz help with my homework
    15·1 answer
  • 50 pts and brainliest if correct
    13·2 answers
  • Solve each equation.
    8·2 answers
  • What is the area of the label on a soup can that is 8 inches high and has a diameter of 4 inches? Round to the nearest hundredth
    5·1 answer
  • Evaluate the following expression using the reverse Polish form<br> 93-4x6 4x82+
    6·1 answer
  • What is the angle of rotation of the image?<br> A. 60°<br> B. 90<br> C. 120<br> D. 180
    13·1 answer
  • Please help with these questions!! Tysm!
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!