a+2b = 2   2a -3b = 4   find a and b.

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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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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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