Problem #19: (3 points) Solve the system below using the substitution method $x + y = 4$ a) $x^2 + y^2 = 16$ b) According to your answer do the two graphs intersect? C) Why?
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Let's solve for y: y=4-x. Now we can substitute this expression for y into the equation x^2+y^2=16: x^2+(4-x)^2=16. Expanding the square, we get x^2+16-8x+x^2=16, which simplifies to 2x^2-8x=0. Factoring out 2x, we get 2x(x-4)=0, so either x=0 or x=4. If x=0, then Show more…
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