Question

Solve the following systems of equations.
$x^2+y^2=25-2xy,y(x+y)=10$

Answer 1

Given that $x^2+y^2=25-2xy$

$x^2+y^2+2xy=25$

$(x+y{)}^2=25$

$(x+y)=5$

Now, $y(x+y)=10$

Put the value of $(x+y)=5$ in above equation

$\Rightarrow y\left(5\right)=10$

$\Rightarrow y=\frac{10}{5}=2$

$\Rightarrow x=3$