Question

Which of the systems of equations below is equivalent to the system shown?

4x + 5y = 3
2x + 3y = 1

A. 4x + 5y = 3
−4x − 6y = 2
B. 12x + 15y = 9
−12x + 18y = 6
C. 4x + 5y = 3
−4x − 3y = 1
D. 12x + 15y = 9
−12x − 18y = −6

Answer 1

`D.....is\: the \: equivalent \: system`

Explanation:

`if \to 4x + 5y = 3 \\ if \to 2x + 3y = 1 \\then \\ 2 * \: 4x + 5y = 3 \\ 4 * 2x + 3y = 1 \\ 10y - 12y = 6 - 4 \\ - 2y = 2 \\ \boxed{ y = - 1} \\ 4x + 5y = 3 \\ 4x +5( - 1) = 3 \\ 4x - 5 = 3 \\ 4x = 3 + 5 \\ 4x = 8 \\ \boxed{x = 2} \\ hence \: the \: equivalent \: system \: is \to D \\`