Question

Which of the following systems is equivalent to the given system?

1/2x - 1/5y = 2
x+ 2/3 y = 5

A: 5 x - 2 y = 20 and 3 x + 2 y = 5
B: 5 x - 2 y = 20 and 3 x + 2 y = 15
C: 2 x - 2 y = 20 and 3 x + 2 y = 5

Answer 1

B) 5x - 2y = 20 and 3x + 2y = 15

Step-by-step explanation:

Rewrite both equations in standard form:

Equation 1

`(1)/(2)x-(1)/(5)y=2`

Multiply both sides by 10:

`\implies (1 \cdot 10)/(2)x-(1 \cdot 10)/(5)y=2 \cdot 10`

`\implies (10)/(2)x-(10)/(5)y=20`

`\implies 5x-2y=20`

Equation 2

`x+(2)/(3)y=5`

Multiply both sides by 3:

`\implies x \cdot 3+(2 \cdot 3)/(3)y=5 \cdot 3`

`\implies 3x+2y=15`

Therefore, the equivalent system is:

5x - 2y = 20 and 3x + 2y = 15

Answer 2

Option B is correct.

Step-by-step explanation:

1st Equation

Remove the denominators:

`\sf \rightarrow (1)/(2)x - (1)/(5) y = 2`

make the denominator's same

`\sf \rightarrow (5)/(10)x - (2)/(10) y = 2`

Join the fraction's:

`\sf \rightarrow (5x-2y)/(10) = 2`

Multiply both sides by 10

`\sf \rightarrow {5x-2y} = 20`

2nd Equation

Remove the denominators:

`\rightarrow \sf x + (2)/(3)y =5`

make the denominator's same

`\rightarrow \sf (3x)/(3) + (2)/(3)y =5`

Join the fraction's:

`\rightarrow \sf (3x+2y)/(3) =5`

Multiply both sides by 3

`\rightarrow \sf 3x+2y} =15`