# if 2a - 3c = 8 and a/2 = (2c+1)/3, find a and c.

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### 1 Answer

Given that :

2a - 3c = 8 .................(1)

a/2 = (2c+1)/3

Let us multiply by 6:

==> 6a/2 = 6(2c+1)/3

==> 3a = 2(2c+1)

==> 3a = 4c + 2

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

Now we will solve the system using the elimination method.

-3*(1) + 1*(2):

==> -6a + 9c = -24

==> 6a - 8c = 4

**==> c = -20.**

Now we will substitute in (1).

==> 2a- 3c = 8

==> 2a - 3(-20) = 8

==> 2a + 60 = 8

==> 2a = -52

**==> a = - 26**

**Then, the answer is: a = -26 and c = -20**