Answer: In mathematics, a variable is a symbol which functions as a placeholder for varying expression or quantities, and is often used to represent an arbitrary element of a set. In addition to numbers, variables are commonly used to represent vectors, matrices and functions
Step-by-step explanation:A symbol for a value we don't know yet. It is usually a letter like x or y.
Example: in x + 2 = 6, x is the variable.
Why "variable" when it may have just one value? In the case of x + 2 = 6 we can solve it to find that x = 4. But in something like y = x + 2 (a linear equation) x can have many values. In general it is much easier to always call it a variable even though in some cases it is a single value.
Answer:
Rate of change = -30
Initial value = 400
Step-by-step explanation:
Write the equation of the linear function representing this situation. Let
x = number of weeks Gandalf is spending money
y = amount of quibbles left in his account.
Gandalf has 400 quibbles in his account. This means, 
is the initial value of quibbles Gandalf had in his account
He spends 30 quibbles each week, this means, that he spends 30x quibbles in x weeks and the amount left in his account is
Therefore, the slope is 
and this is the rate of change (negative because the amount of money in his account decreases each week)
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Answer:
it is 36.75
Step-by-step explanation:
Since you need an isolated variable to use the substitution method, we need to re-arrange one of the equations. This will probably be easiest to do with the first one.
Add 5y to both sides of the first equation.
x=10+5y
Now, in the second equation, put in 10+5y in any spot that has an x.
2(10+5y)-10y=20
Distribute the 2 to both numbers in the parenthesis.
20+10y-10y=20
Combine like terms.
20=20
This means that the two equations are actually the same. You can see this if you multiply the whole first equation by 2
2(x-5y=10)
2x-10y=20, which is the same as the second equation. Therefore, the two equations are actually the same one.
