Answer:
29520728184915396206153835295
Answer:
3:7
Step-by-step explanation:
So to solve this problem, you have to understand what the ratio 1:4 and 2:3 means. The 1:4 ratio in the first equation means that for "each unit of alcohol" there is 4 of those units of water. So let's say I had 2 gallons of alcohol and mixed it with 8 gallons of water. This means for each gallon of alcohol, there is 4 gallons of water, or in other words a 1:4 ratio. This can be described as a percentage as well. For each 5 gallons there are 4 gallons of water, and 1 gallon of alcohol or <em>20%</em> is alcohol. So let's just say that x=alcohol and y=water, this means that:
where c is the total amount in the glass. This means that: 
Let's do the same thing to the second equation. the ratio means that for every 2 units of alcohol there are 3 units of water. This means for every 5 gallons of the mixture there is 2 units of alcohol which is 40%. In this case let's also say that j=alcohol and k=water. This means that:
and that:
.
So if we're going to add the two glasses, we simply add the two sides, and get:
. Now remember how can can express j and x in terms of c, since it's a certain percentage of c (the entire thing). This means that we get:
Now we can add like terms to get the equation:
. We can find how much 0.6c is to 2c by dividing the 2, in doing so we get that 0.6c/2c = 0.3, or in other words the 0.6c is only 30% of the final mixture, and since the 0.6c represents the alcohol in this mixture, that means that's the percentage of alcohol. To write this as a ratio, this means for every 3 units of alcohol, there is 7 units of water, because 3/10 = 30%.
2x-4y=-16
ax+4y=6 +
--------------------
2x+ax=-10; for x=-2,
2(-2)+a(-2)=-10
-2a=-10+4
a=-6/-2
a=3
Answer:
<em>(a) x=2, y=-1</em>
<em>(b) x=2, y=2</em>
<em>(c)</em> 
<em>(d) x=-2, y=-7</em>
Step-by-step explanation:
<u>Cramer's Rule</u>
It's a predetermined sequence of steps to solve a system of equations. It's a preferred technique to be implemented in automatic digital solutions because it's easy to structure and generalize.
It uses the concept of determinants, as explained below. Suppose we have a 2x2 system of equations like:

We call the determinant of the system

We also define:

And

The solution for x and y is


(a) The system to solve is

Calculating:





The solution is x=2, y=-1
(b) The system to solve is

Calculating:





The solution is x=2, y=2
(c) The system to solve is

Calculating:





The solution is

(d) The system to solve is

Calculating:





The solution is x=-2, y=-7