If (x,y) is a solution to the system of equations shown, what is the product of the y-coordinates of the solutions? x^(2)+4y^(2)=40 x+2y=8

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If  (x,y) is a solution to the system of equations shown, what is the product of the  y-coordinates of the solutions?  x^(2)+4y^(2)=40  x+2y=8

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Solve linear equation for x: Solve the linear equation for x. The linear equation is x + 2y = 8. We can solve for x by isolating it on one side of the equation. x = 8 - 2ySubstitute expression for x into quadratic equation: Substitute the expression for x into the quadratic equation. The quadratic equation is x^2 + 4y^2 = 40. We substitute x = 8 - 2y into this equation to get: (8 - 2y)^2 + 4y^2 = 40Expand and simplify the equation: Expand the squared term and simplify the equation. Expanding (8 - 2y)^2 gives us 64 - 32y + 4y^2. Now we have: 64 - 32y + 4y^2 + 4y^2 = 40 Combine like terms to get: 64 - 32y + 8y^2 = 40Move all terms to one side: Move all terms to one side to set the equation to zero. Subtract 40 from both sides to get: 8y^2 - 32y + 24 = 0Simplify the equation by dividing all terms: Simplify the equation by dividing all terms by 8. Dividing each term by 8 gives us: y^2 - 4y + 3 = 0Factor the quadratic equation: Factor the quadratic equation. The equation y^2 - 4y + 3 factors into: (y - 3)(y - 1) = 0Solve for y: Solve for y by setting each factor equal to zero. Setting each factor equal to zero gives us two possible y-values: y - 3 = 0  or  y - 1 = 0 So, y = 3 or y = 1Find the product of the y-coordinates: Find the product of the y-coordinates. The product of the y-coordinates of the solutions is: 3 * 1 = 3

If $(x, y)$ is a solution to the system of equations shown, what is the product of the $y$ -coordinates of the solutions? $\newline$ $x^{2}+4 y^{2}=40$ $\newline$ $x+2 y=8$

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If (x,y) (x, y) (x,y) is a solution to the system of equations shown, what is the product of the y y y-coordinates of the solutions?\newlinex2+4y2=40 x^{2}+4 y^{2}=40 x2+4y2=40\newlinex+2y=8 x+2 y=8 x+2y=8

If $(x, y)$ is a solution to the system of equations shown, what is the product of the $y$ -coordinates of the solutions? $\newline$ $x^{2}+4 y^{2}=40$ $\newline$ $x+2 y=8$