Question

Solve the system of equations.
$x^2+y^2=25$, $x-y=5$

• A. $(-5,0)$ only
• B. $(0,5)$ only
• C. $(0,-5)$ and $(-5,0)$
• D. $(0,5)$ and $(5,0)$
• E. $(0,-5)$ and $(5,0)$

Answer 1

The correct option is E $(0,-5)$ and $(5,0)$

Given equations are $x^2+y^2=25$ and $x-y=5$

From second equation, $y=x-5$

$\Rightarrow x^2+{(x-5)}^2=25$ (When substituted in first equation):

$\Rightarrow x^2+x^2-10x+25=25$

$\Rightarrow 2x^2-10x=0$

$\Rightarrow x^2-5x=0$

$\Rightarrow \left(x\right)(x-5)=0$

$\Rightarrow x=0,5$

When $x=0,y=0-5=-5$

When $x=+5,y=5-5=0$

Points of intersection are $(0,-5)(5,0)$.