Which system of equations has the same solution as the system below?
4x+ 5y = 13
10x - 8y = -32

A 4x+ 5y= 13
5x - 4y = -32
B 40x + 50y = 130
5x - 4y = 16
C 20x + 25y = 65
-20x + 16y = 64
D -4x - 5y = 13
10x - 8y = -32

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

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step-by-step explanation: