Question

Solve the system by the elimination method.

3x - 2y - 7 = 0
5x + y - 3 = 0
To eliminate y, the LCM is 2. Which of the following is the resulting equations?

1.3x - 2y - 7 = 0
5x + y - 3 = 0

2.3x - 2y - 7 = 0
-10x - 2y + 6 = 0


3.3x - 2y - 7 = 0
10x + 2y - 6 = 0

Answer 1

`\large\boxed{\left\{\begin{array}{ccc}3x-2y-7=0\\10x+2y-6=0\end{array}\right}`

Explanation:

`\left\{\begin{array}{ccc}3x-2y-7=0\\5x+y-3=0&\text{multiply both sides by 2}\end{array}\right\\\\\boxed{\underline{+\left\{\begin{array}{ccc}3x-2y-7=0\\10x+2y-6=0\end{array}\right}}\qquad\text{add both sides of the equations}\\.\qquad\qquad13x-13=0\qquad\text{add 13 to both sides}\\.\qquad\qquad 13x=13\qquad\text{divide both sides by 13}\\.\qquad\qquad x=1\\\\\text{put the value of x to the second equation:}\\\\5(1)+y-3=0\\(5-3)+y=0\\2+y=0\qquad\text{subtract 2 from both sides}\\y=-2\\\\\boxed{x=1,\ y=-2}`