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

Answer:

Option B is correct.

Explanation:

1st Equation

Remove the denominators:

$\sf \rightarrow \dfrac{1}{2}x - \dfrac{1}{5} y = 2$

make the denominator's same

$\sf \rightarrow \dfrac{5}{10}x - \dfrac{2}{10} y = 2$

Join the fraction's:

$\sf \rightarrow \dfrac{5x-2y}{10} = 2$

Multiply both sides by 10

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

2nd Equation

Remove the denominators:

$\rightarrow \sf x + \dfrac{2}{3}y =5$

make the denominator's same

$\rightarrow \sf \dfrac{3x}{3} + \dfrac{2}{3}y =5$

Join the fraction's:

$\rightarrow \sf \dfrac{3x+2y}{3} =5$

Multiply both sides by 3

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

Answer 2

Answer:

B)  5x - 2y = 20  and  3x + 2y = 15

Step-by-step explanation:

Rewrite both equations in standard form:

Equation 1

$\dfrac{1}{2}x-\dfrac{1}{5}y=2$

Multiply both sides by 10:

$\implies \dfrac{1 \cdot 10}{2}x-\dfrac{1 \cdot 10}{5}y=2 \cdot 10$

$\implies \dfrac{10}{2}x-\dfrac{10}{5}y=20$

$\implies 5x-2y=20$

Equation 2

$x+\dfrac{2}{3}y=5$

Multiply both sides by 3:

$\implies x \cdot 3+\dfrac{2 \cdot 3}{3}y=5 \cdot 3$

$\implies 3x+2y=15$

Therefore, the equivalent system is:

5x - 2y = 20  and  3x + 2y = 15