To solve for 12a given the equations 4a + 6b = 10 and 2a + 4b = 12, we can start by manipulating these equations to express them in terms of ‘a’ and ‘b’.
First, let’s simplify the second equation:
2a + 4b = 12
By dividing everything by 2, we get:
a + 2b = 6
Now, we will use this simplified equation to substitute ‘b’ in the first equation:
From a + 2b = 6, we can express ‘b’ as:
2b = 6 – a
b = (6 – a)/2
Substituting ‘b’ into the first equation:
4a + 6((6 – a)/2) = 10
4a + 3(6 – a) = 10
4a + 18 – 3a = 10
a + 18 = 10
Now, isolating ‘a’:
a = 10 – 18
a = -8
Now that we have the value of ‘a’, we can substitute back to find ‘b’. Using ‘a + 2b = 6’:
-8 + 2b = 6
2b = 6 + 8
2b = 14
b = 7
Now we have the values of ‘a’ and ‘b’, so we can find 12a:
12a = 12 * (-8) = -96
Therefore, the answer is:
12a = -96