Question

2/3x - 1/2y = 3

1/2x + y = 5
Which of the following systems is equivalent to the given system?
2x - y = 18 and x + 2y = 10
4x - 3y = 18 and x + 2y = 10
2x - 3y = 3 and x + 2y = 5

Answer 1

The second one, 4x - 3y = 18 and x + 2y = 10

Explanation:

You should find the equation that corresponds to original one, multiplying both sides by the same number.

This operation has to be done with the two equations of the system.

So, let's check first equation 2/3x - 1/2y = 3

2/3x - 1/2y = 3 multiplying both sides by 6

`((2)/(3) x*6)-((1)/(2) y*6)=3*6\\4x-3y=18`

Next, let's check second equation 1/2x + y = 5

1/2x + y = 5 multiplying both sides by 2

`((1)/(2) x*2)+(y*2)=5*2\\x+2y=10`

Answer 2

The correct answer for this question would be the second option. 4x - 3y = 18 and x + 2y = 10. So in order to know why this is the answer, let us check it. Since the given numbers have fractions, let us eliminate the fractions.
2/3x - 1/2 y = 3 <<multiply both sides by 6
and we get 4x - 3y = 18 (So this one is correct)
Next,
1/2x + y = 5 << multiply both sides by 2 and we get
x + 2y = 10 (This one is correct too)
Hope this answer helps.