Question

Select the best possible first step to solving the system by first eliminating the x variable.3x − 9y = 6 2x − 11y = 6?

Answer 1

`\left\{\begin{array}{ccc}3x-9y=6&|divide\ both\ sides\ by\ 3\\2x-11y=6&|divide\ both\ sides\ by\ (-2)\end{array}\right\\\\\underline{+ \left\{\begin{array}{ccc}x-3y=2\\-x+5.5y=-3\end{array}\right}\\.\ \ \ 2.5y=-1`

Answer 2

x=4/5

y=-2/5

Explanation:

We have two equations:

`3\cdotx-9\cdoty=6`

`2\cdotx-11\cdoty=6`

We can eliminate x by making x of equation 1 be equal to x in the equation 2:

`x=2+3\cdoty`

Substitute into equation 2:

`2\cdot(2+3\cdoty)-11\cdoty=6`

Simplify:

`2\cdot2+2\cdot3\cdoty-11\cdoty=6`

`4+6\cdoty-11\cdoty=6`

`-5\cdoty=2`

`y=-2/5`

Substitute back into one of the equations:

`x=2+3\cdot(-2/5)`

`x=2-6/5`

`x=10/5-6/5=4/5`