There are no solutions to this system. If
the line is positive and the exponential is negative, so they can't have any point in common.
At 
, the derivative of the line is 
, whereas the derivative of the exponential is 
.
Since 
for all 
, there can't be other solutions because the exponential is already below the line, and it decreases at a faster rate.
To get the common denominator, we need to get the multiples of each denominator.
multiples of 6 : 6, 12, 18
multiples of 3 : 3, 6, 9, 12
multiples of 4 : 4, 8, 12
The common multiple 12. So, we need to multiply each fraction by the corresponding number that will result to a product of 12 in the denominator. Whatever number is multiplied to the denominator must also be the number multiplied to the numerator.
1/6 * 2/2 = 2/12
1/3 * 4/4 = 4/12
3/4 * 3/3 = 9/12
Since the denominator is already common, we use the numerator to arrange it in order from least to greatest. 2 is lesser than 4 and 4 is less than 9.
So, order from least to greatest ⇒ 1/6 , 1/3, and 3/4
Standard form is written Ax + By = C where A, B, and C are all integers.
In other words, no fractions.
Also, the A or the coefficient of the x term must be positive.
The only thing we need to do is add 7x to both sides to get 7x + y = -1.
So 7x + y = -1 is our answer.
