10 question of spelling words and 16 questions of vocabulary are present
Solution:
Let "x" be the number of spelling word questions
Let "y" be the number of vocabulary word question
There is a total of 26 questions. Therefore, we get
number of spelling word questions + number of vocabulary word question = 26
x + y = 26 --------- eqn 1
There are spelling word questions that worth 2 points each and vocabulary word question worth 5 points each
The language arts test is worth 100 points
Therefore, we frame a equation as:
number of spelling word questions x 2 + number of vocabulary word question x 5 = 100
2x + 5y = 100 --------- eqn 2
Let us solve eqn 1 and eqn 2
From eqn 1,
x = 26 - y ------- eqn 3
Substitute eqn 3 in eqn 2
2(26 - y) + 5y = 100
52 - 2y + 5y = 100
3y = 100 - 52
3y = 48
y = 16
Substitute y = 16 in eqn 3
x = 26 - 16
x = 10
Thus 10 question of spelling words and 16 questions of vocabulary are present