Question

15PTS QUICK

Answer 1

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