Verified answer

x= 2 point questions

y=4 point questions

x+y=40

2x+4y=100

From the first equation x=40-y

substitute in second equation for x

2(40-y)+4y=100

80-2y+4y=100

2y=20

y=10

Substitute 10 for y in either equation

x+10=40

x=30

30 2 point questions

10 4 point questions

Let a = number of two-point questions, b = number of four-point questions. Then:

a + b = 40 (there are forty questions)

2a + 4b = 100 (the total points are 100)

Since a + b = 40, b = 40 - a. Substitute 40 - a for b in the second equation:

2a + 4(40 - a) = 100

2a + 160 - 4a = 100 by multiplying each term inside the parentheses by the 4 outside them

2a - 4a = 100 - 160 by subtracting 160 from each side

-2a = -60 by performing the subtractions on each side

a = -60 / (-2) by dividing each side by -2

a = 30 by performing the division on the right side

There are 30 two-point questions. Since there are 40 questions in all, there are 10 four-point questions. 30 two-point questions give 60 points. 10 four-point questions give 40 points. 60 points plus 40 points is 100 points.

Number of 2 point questions is x. Number of 4 point questions is y.

2x + 4y = 100, and

x + y = 40

(^^multiply by 2) -----> 2x + 2y = 80

Then subtract this from first equation and get 2y = 20, sooo...

y = 10 and, then solve for x

x = 30