Answer:
Option B
40x + 50y = 130
5x - 4y = 16
Option C
20x + 25y = 65
-20x + 16y = 64
Step-by-step explanation:
we have
4x+5y=13 ----> equation a
10x-8y=-32 ----> equation b
we know that
If two system of equations are equivalent, then their solution is the same
Part 1)
step 1
Multiply by 10 equation a both sides
10(4x+5y)=10(13)
40x+50y=130 ----> equation a'
step 2
Divide by 2 equation b both sides
(1/2)(10x-8y)=(1/2)(-32)
5x-4y=-16 ----> equation b'
so
The system of equations a and b and the system of equations a' and b' are equivalent
therefore
The system of equations a' and b' have the same solution as the given system
Part 2)
step 1
Multiply by 5 equation a both sides
5(4x+5y)=5(13)
20x+25y=65 ----> equation a'
step 2
Multiply by -2 equation b both sides
-2(10x-8y)=-2(-32)
-20x+16y=64 ----> equation b'
so
The system of equations a and b and the system of equations a' and b' are equivalent
therefore
The system of equations a' and b' have the same solution as the given system
