Answer:
10 five-point questions and 40 two-point questions
Step-by-step explanation:
Let x represent the total number of five-point questions and y represent the total number of two-point questions.
Equation 1: 5x+2y=130
Equation 2: x+y=50
Multiplying Equation 2 by 2: 2x+2y=100 (Equation 3)
(Equation 1) - (Equation 3): 3x=30
x=10
Substituting x=10 into x+y=50: 10+y=50
y=40
Therefore, there are 10 five-point questions and 40 two-point questions.
Check
Substituting x=10 and y=40 into Equation 1:
LHS=5x+2y=5(10)+2(40)=50+80=130
RHS=130
LHS=RHS
Substituting x=10 and y=40 into Equation 2:
LHS=x+y=10+40=50
RHS=50
LHS=RHS
Since in both cases the left-hand side is equal to the right-hand side, the answer is correct.
(LHS: left-hand side, RHS: right-hand side)
