What do the two variables represent?
The two variables represent the number of nights or squires at the jousting contest.
Write a system of equations.
let k = number of knights and let s = number of squires
3k + 2s = 32
2k + s = 19
How many knights are there? 6
How many squires are there? 7
Solving:
solve for s in the second equation by subtracting 2k from both sides
2k + s = 19
s = 19 - 2k
substitute into first equation
3k + 2(19-2k) = 32
distribute 2 into 19-2k
3k + 38 - 4k = 32
add like terms
-k + 38 = 32
subtract 38 from both sides
-k = -6
divide by -1
k = 6
subsitute into the equation for s
s = 19 - 2k
s = 19 - 2(6)
s = 19 - 12
s = 7
