konyinsammy1
Answered

Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

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

Sagot :

devishri1977

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    -10a + 6b = -6  {Now add}

            -a            = -3

                       a = -3/(-1)

        [tex]\sf \boxed{a = 3}[/tex]

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_}

          [tex]\sf \boxed{b = 4}[/tex]                      

sqdancefan

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.

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.