Question

Solve the Problem using elimination by addition

$2 m-n=10$

$m-2 n--4$

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 3We will multiply the second equation by $2$:

$\begin{align*} 2\cdot(m-2n)&=2\cdot(-4)\\ 2m-4n&=-8 \end{align*}$

The given system is equivalent to the following system:

$\begin{align*} 2m-n&=10 &&(1)\\ 2m-4n&=-8 &&(2) \end{align*}$

Now, let us substract the equation $(2)$ from $(1)$

$\begin{align*} 2m-n-(2m-4n)&=10-(-8)\\ \cancel{2m}-n-\cancel{2m}+4n&=10+8\\ 3n&=18\\ n&=6 \end{align*}$

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