Answer
$x_{1}=12$
$x_{2}=-7$
Work Step by Step
This problem requires alot of manipulation of the variables.
To start, divide the first equation by two so that you can begin to eliminate $x_{1}$.
$\frac{(2x_{1}+4x_{2})}{2}=\frac{-4}{2}$
$x_{1}+2x_{2}=-2$
Now you can freely manipulate $x_{1}$, as in you can now set the constant of $x_{1}$ to whatever you would like. For example, you can multiply the equation by 10 to change $x_{1}$ to $10x_{1}$. We will use this to eliminate $x_{1}$ and isolate $x_{2}$.
We know that in the second equation, $x_{1}$ is multiplied by $5$, so if we multiply the first equation by 5, we can eliminate $x_{1}$.
$5*(x_{1}+2x_{2})=5*(-2)$
$5x_{1}+10x_{2}=-10$
And now subtract one equation from the other.
$(5x_{1}+7x_{2}=11)$
$-(5x_{1}+10x_{2}=-10)$
And you will get $-3x_{2}=21$, and you can solve for $x_{2}$.
$-3x_{2}=21$
$x_{2}=\frac{21}{-3}=-7$
Now you can find $x_{1}$ through substitution.
$2x_{1}+4x_{2}=-4$
$2x_{1}+4(-7)=-4$ (Substitution)
$2x_{1}-28=-4$
$2x_{1}=-4+28=24$ (Getting $x_{1}$ alone)
$x_{1}=\frac{24}{2}=12$ (Solving for $x_{1}$)
Lastly, check by substituting into the other equation.
$5x_{1}+7x_{2}=11$
$5(12)+7(-7)=11$ (Substitution)
$60-49=11$
$11=11$
The values work and are therefore the answers.
Same principle is used in this one, only this one had a bit more manipulation.
