Solve the following system by the elimination method Check t

Solve the following system by the elimination method. Check the solution. 2x + 3y = 0 10x + 18 = 6y Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The system has a single solution. The solution set is {}. (Type an ordered pair, using integers or fractions.) There are infinitely many solutions. The solution set is {(x, y)|}. (Type an equation. Type your answer in standard form.) The solution set is the empty set.

Solution

Given system of equations :

2x+ 3y = 0 ------ (i)

10x + 18 = 6y ------ (ii)

Multiplying the first equation by -5

-10x - 15y = 0

10x - 6y = -18

Adding the above two equation will give us the value of y

( -10x - 15y) + (10x - 6y ) = 0 -18

-21 y = -18

y = 18/21

y = 6/7

substitute the value for y into the original equation to solve for x

2x+ 3y = 0   

2x + 3 ( 6/7) = 0

2x = - 18/7

x = -9/7

Option A is the correct answer

The system has a single solution , The solution set is ( -9/7 , 6/7)