Pl0x

a math test is worth 100 points. there are a total of 26 questions. there are equation questions that are worth 2 points each and vocabulary questions are 5 points each.

use a system of equations to solve for the number of equation questions and vocabulary questions on the math test. show all work for full credit.

E=equation questions
v=vocab questions

26 questions
e+v=26

total 10 points
2e+5v=100

so we gots

e+v=26 and
2e+5v=100

elimination
multiply first equation by -2 and add to 2nd equation

-2e-2v=-52
2e+5v=100 +
0e+3v=48

3v=48
divide both sides by 3
v=16

sub back

e+v=26
e+16=26
minus 16 both sides
e=10

10 equation questions
16 vocab questions

Let the number of equations be x and the number of vocabulary questions be y.

x + y = 26 (total num of questions)
So, y = 26 - x (eliminate one variable to solve for one first)
2x + 5y = 100 (total points)
2x + 5 (26 - x) = 100 (substituting 26 - x in place of y)

2x + 130 - 5x = 100 (distributing the 5)
-3x = -30
x = 10

Since there are 10 equation questions, there must be 16 vocabulary questions to satisfy the total number of questions in the test.