Solve the linear system of equations using the linear combination method. {8a−4b=205a−8b=62
1 answer:
Step 1:
Line up respective variables in column.
.................(1)
.................................(2)
Step 2:
We need to multiply first equation with -2 so that the coefficient of b becomes equal and opposite of -8.
*2
...................(3)
Step 3:
Add equation (2) and (3)
The b terms will cancel out and we are left with only a terms.
-11a = 22
dividing both sides by -11
a=-2
Step 4:
plug this value of a in equation (1) to find value of b,
b=-9
Answer : a=-2 and b =-9
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The unknown b is stuck in the exponent position.
We can can fix that by using logarithms.
Log is the inverse operation of the exponential.
We'll take log of each side.
Log of what base tho?
Well, the base of our exponential is e,
so we'll take log base e of each side.
We'll apply one of our log rules next:
This allows us to take the exponent out of the log,
Another thing to remember about logs:
When the base of the log matches the inside of the log,
then the whole thing is simply 1,
So our equation simplifies to this,
As a final step, divide both sides by 3,
k, hope that helps!