Question

What is the solution of the system?


Use the elimination method.

4x+2y=6
6x−4y=−12


A The solution is (3/2,  0)

B The solution is (0, 3) .

C There are an infinite number of solutions.

D There is no solution.

Answer 1

B. the solution is (0, 3)

Answer 2

given equations are

$4x + 2y = 6......(1) \\ \\ 6x - 4y = - 12........(2) \\ \\ \\ mltiplying \: the \: equaton \: (1) \: by \: 3 \\ \\ 12x + 6y = 18........(3) \\ \\ and \: multiplying \: the \: equation \: (2) \: by \: 2 \\ \\ 12x - 8y = - 24......(4) \\ \\ now \: subtract \: the \: equation \:( 4) \: from \: equation \: (3) \\ \\ 12x + 6y - (12x - 8y) = 18 - ( - 24) \\ \\ = > 12x + 6y - 12x + 8y = 18 + 24 \\ \\ = > 14y = 42 \\ \\ = > y = \frac{42}{14 } \\ \\ = > y = 3 \\ \\ \\ now \: multiplying \: the \: equation \: (1) \: by \: 2 \\ \\ 8x + 4y = 12......(5) \\ \\ now \: adding \: the \: equation \: (2) \: and \: equation \: (5) \\ \\ \\ 6x - 4y + 8x + 4y = - 12 + 12 \\ \\ = > 14x = 0 \\ \\ x = \frac{0}{14} \\ \\ = > x = 0 \\ \\ therefore \\ \\ x = 0 \: and \: y = 3$

so option B(0, 3) is right answer.

hope it helps.....