Question

-5x-5y=0 and y=8xI need help solving this systems of equations using elimination.

Answer 1

(0, 0)

Step-by-step explanation

To solve this system by elimination, one of the variables must have the same coefficient or opposite coefficients in both equations. If this condition is not given, we can divide and/or multiply one or both equations by a constant to make this condition true.

First, we have to divide the first equation by 5,

`\begin{gathered} (-5x)/(5)-(5y)/(5)=(0)/(5) \\ -x-y=0 \end{gathered}`

Also, subtract 8x from both sides of the second equation,

`\begin{gathered} y-8x=8x-8x \\ -8x+y=0 \end{gathered}`

Now, this new system is equivalent - i.e. it has the same solution, as the given system,

`\begin{cases}-x-y=0 \\ -8x+y=0\end{cases}`

To solve by elimination, now we add the two equations. This will eliminate the y-variable,

Find x from this equation. Note that the equation is x multiplied by a constant is equal to 0. This means that the solution is x = 0.

Now, to find the y-coordinate of the solution we have to replace x with 0 in one of the equations of the system. The second equation is already solved for y, so replace x there,

`y=8x=8\cdot0=0`

Hence, the solution is (0, 0).