Question

Use elimination to find x-coordinate of the solution of the system 9x-8y=2 -3x-9y=-24

Answer 1

`\left\{\begin{array}{ccc}9x-8y=2\\-3x-9y=-24&\text{multiply both sides by 3}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}9x-8y=2\\-9x-27y=-72\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad-35y=-70\qquad\text{divide both sides by (-35)}\\.\qquad\qquad\boxed{y=2}\\\\\text{Put the value of y to the second equation}:\\\\-3x-9(2)=-24\\-3x-18=-24\qquad\text{add 18 to both sides}\\-3x=-6\qquad\text{divide both sides by (-3)}\\\boxed{x=2}\\\\Answer:\ \boxed{x=2}`

Answer 2

x coordinate is 2

Explanation:

We have given,

9x - 8y = 2 .........(1)

-3x - 9y = -24 ...............(2)

We use elimination method to eliminate y.

We multiply equation (1) by 9 and equation (2) by 8.

We get,

{ 9x - 8y = 2} × 9 or 81x - 72y = 18 -------------(3)

{-3x - 9y = - 24} × 8 or -24x - 72y = -192 -----------(4)

And subtract equation (4) from equation (3)

So , (81x - 72y ) - (-24x -72y)= 18 -(-192)

or 105x = 210

or x = 210/105

or x= 2

Hence we get x coordinate as x= 2