Question

Where do theses two lines intersect?
x^2+y^2=49
y=-2X+2
(I completed partial Work, don't fully understand matrix equation)

Answer 1

Well, they aren't both lines. One is the equation of a circle with radius 7. Either way, solving this just requires you plug in y into the circle equation. This gives:
\[x^2+(-2x+2)^2=49 \implies x^2+4x^2+4-8x=49 \implies 5x^2-8x-45=0\]
Using the quadratic equation we find that:
\[x= \frac{4 \pm \sqrt{241}}{5}\]
Plug this into the y equation to solve for y.