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What are the $y$ coordinates of the system, $x^2+y^2=10$ and $x-2y=5$

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Full solution

Q. What are the

y

coordinates of the system,

x^2+y^2=10

and

x-2y=5

Solve for x: Step $1$ : Solve the line equation for x. $\newline$ $x - 2y = 5$ $\newline$ $x = 2y + 5$
Substitute in circle equation: Step $2$ : Substitute $x$ in the circle equation. $(2y + 5)^2 + y^2 = 10$ $4y^2 + 20y + 25 + y^2 = 10$ $5y^2 + 20y + 25 = 10$
Simplify and solve quadratic: Step $3$ : Simplify and solve the quadratic equation. $\newline$ $5y^2 + 20y + 15 = 0$ $\newline$ $y^2 + 4y + 3 = 0$ $\newline$ $(y + 3)(y + 1) = 0$ $\newline$ $y = -3$ , $y = -1$

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