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a+2b = 2   2a -3b = 4   find a and b.

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clara2 | Student, Undergraduate | (Level 3) eNoter

Posted January 18, 2011 at 11:47 AM via web

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a+2b = 2   2a -3b = 4   find a and b.

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neela | High School Teacher | (Level 3) Valedictorian

Posted January 18, 2011 at 12:17 PM (Answer #1)

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Q;

a+2b = 2.......(1)

2a -3b = 4 ....(2)

We have to find a and b.

Solution:

2*(1)-(2):  2(a+2b) - (2a-3b) = 2*2-4 = 0.

4b+3b = 0.

7b = 0.

7b/7 = 0/7.

b= 0.

We put b= 0 in (1): a+2b = 2. So a+2*0 = 2. So a = 2.

a =  2 and b = 0.

a = 2.  b = 0.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted January 18, 2011 at 11:50 AM (Answer #2)

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a + 2b = 2 ................(1)

2a -3b = 4 .................(2)

We will use the elimination method to solve.

We will multiply (1) by -2 and add to (2).

==> -2a -4b = -4 .....................-2*(1)

==>  2a -3b = 4 .....................(2)

==> -7b = 0 ==> b= 0

Now to calculate a we will substitute into (1).

==> a + 2b = 2 ==> a + 0 + 2 ==> a = 2

==> a = 2

Then the answer to the system is :

a = 2   and   b= 0

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted January 18, 2011 at 12:04 PM (Answer #3)

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We have to solve for a and b given a + 2b = 2 and  2a -3b = 4

a + 2b = 2

=> a = 2 - 2b

Substitute this in 2a - 3b = 4

=> 2( 2 - 2b) - 3b = 4

=> 4 - 4b - 3b = 4

=> -7b = 0

=> b = 0

a = 2 - 2b = 2

Therefore a = 2 and b = 0

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