Question

Use elimination to solve for x and y:
- 2x - y = 9
2x - 9y = 1

Answer 1

x=-4, y=-1

Explanation:

Given the following system of equations, solve the system using elimination.

`\left \{ {{-2x-y=9} \atop {2x-9y=1}} \right.`

(1) - Add the equations together

`\left\begin{array}{ccc}&-2x-y=9\\+&2x-9y=1\end{array}\right\\\\\Longrightarrow -10y=10\\\\\therefore \boxed{y=-1}`

Notice how the x term was eliminated, hence the name for this method is "elimination."

(2) - Take the value we just found for y and plug it into either of the two equations and solve for x

`2x-9y=1\\\\\Longrightarrow 2x-9(-1)=1\\\\\Longrightarrow 2x+9=1\\\\\Longrightarrow 2x=-8\\\\\therefore \boxed{x=-4}`

(3) - Thus, the system is solved. When x=-4, y=-1.