Question

How many solutions does this system have? 2 x - 3 y = 10. -4 x + 6 y = - 20.

A) One
B) Two
C) An infinite number
D) No solution

Answer 1

Answer: The correct answer is: [D]: " No solution " .

______________________________________

Explanation:

We are given the following system of equations:

2x − 3y = 10 ;

-4x + 6y = -20 ;

_______________________________________

Let us take the second equation:

-4x + 6y = -20 ;

and multiply each side by "-1 " ; to get rid of the "negative numbers" ; and to rewrite the equation without the "negative numbers" :

- 1 * { - 4x + 6y } = -1 * (-20} ;

to get:

4x − 6y = -20 ;

Now, let us simply this equation further; by divide each side of the equation by "2" ;

(4x − 6y) / 2 = (-20) / 2 ;

→ [ (4x) / 2 ] − [ (6y) / 2 ] = -10 ;

to get: 2x − 3y = -10 ;

Then we have: 2x − 3y = 10 ;

Note: 10 ≠ -10 .

_______________________________________

So the answer is: [D]: " No solution."

_______________________________________

Hope this explanation helps you! Best wishes!

_______________________________________