How do you write a system of linear equation in two variables? Explain this in words and by using mathematical notation in an equation.
Suppose you are given the following problem: Tom has 15 coins, all of them quarters or dimes. He has twice as many dimes as quarters. How many dimes does he have?
(1) Assign variables to the unknowns. Here let x be the number of quarters, y the number of dimes.
(2) Translate the givens into algebraic notation. Since Tom has 15 coins, we know the number of quarters plus the number of dimes is 15 so x+y=15.
Since there are twice as many dimes as quarters we have 2x=y.
(3) Write the two equations:
This is a system of linear equations with two unknowns.
To solve we can use substitution:
x+2x=15 ==> x=5 so y=10.
There are 5 quarters and 10 dimes.
Check: the number of coins is 5+10=15; the number of dimes (10) is twice the number of quarters (5).