Step 1

Let x be the 2 point questions and y be the 5 point questions. Write the equation can be written as the linear equation as given below.

x+y=38...(1)

2x+5y=100...(2)

Multiply equation(1)from equation (2),

2x+2y=76...(3)

Subtract equation(1)from equation(2),

3y=24 \({y}=\frac{24}{{3}}\) (Divide by 3 on both sides)

y=8

Step 2

Substitute 8 for y in equation (1),

x+8=38

x=38-8 (subtract 8 on both sides)

x=30

Thus,there are 30 questions had 2 points and 8 questions had 5 points.

Step 3

Result:

The count of 2 point questions are 30 and 5 point questions are 8.

Let x be the 2 point questions and y be the 5 point questions. Write the equation can be written as the linear equation as given below.

x+y=38...(1)

2x+5y=100...(2)

Multiply equation(1)from equation (2),

2x+2y=76...(3)

Subtract equation(1)from equation(2),

3y=24 \({y}=\frac{24}{{3}}\) (Divide by 3 on both sides)

y=8

Step 2

Substitute 8 for y in equation (1),

x+8=38

x=38-8 (subtract 8 on both sides)

x=30

Thus,there are 30 questions had 2 points and 8 questions had 5 points.

Step 3

Result:

The count of 2 point questions are 30 and 5 point questions are 8.