Question

PLEASE HELP ME

What is the solution to this system of equations?

Two-thirds x + y = 6. Negative two-thirds x minus y = 2.


A) (1, -1)

B) (0, 8)

C) infinitely many solutions

D) no solution

Answer 1

d is right

Explanation:

Answer 2

Option D

The system of equation has no solution

Solution:

Given system of equations:

`(2)/(3)x + y = 6\\\\Simplify\\\\2x + 3y = 18 ------ eqn 1`

`(-2)/(3)x -y = 2\\\\Simplify\\\\-2x -3y = 6 ------- eqn 2`

Solve eqn 1 and eqn 2

Add eqn 1 and eqn 2

2x + 3y -2x - 3y = 18 + 6

2x + 3y = 2x + 3y + 18 + 6

`0\\eq 24`

If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur.

No solution would mean that there is no answer to the equation

Thus the system of equation has no solution