Answer:
Option B
40x + 50y = 130
5x - 4y = 16
Option C
20x + 25y = 65
-20x + 16y = 64
Step-by-step explanation:
we have
[tex]4x+5y=13[/tex] ----> equation a
[tex]10x-8y=-32[/tex] ----> 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
[tex]10(4x+5y)=10(13)[/tex]
[tex]40x+50y=130[/tex] ----> equation a'
step 2
Divide by 2 equation b both sides
[tex](1/2)(10x-8y)=(1/2)(-32)[/tex]
[tex]5x-4y=-16[/tex] ----> 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
[tex]5(4x+5y)=5(13)[/tex]
[tex]20x+25y=65[/tex] ----> equation a'
step 2
Multiply by -2 equation b both sides
[tex]-2(10x-8y)=-2(-32)[/tex]
[tex]-20x+16y=64[/tex] ----> 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
