(x,y) is a solution to the system of equations shown, what is the product of the y-coordinates of the solutions? [x^(2)+y^(2)=9], [x+y=3]

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(x,y) is a solution to the system of equations shown, what is the product of the  y-coordinates of the solutions?  [x^(2)+y^(2)=9], [x+y=3]

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Write Equations: Write down the given system of equations. We have the following system of equations: 1) $ x^2 + y^2 = 9 $ 2) $ x + y = 3 $Solve for y: Solve the second equation for one of the variables. Let's solve for $ y $: $ y = 3 - x $Substitute and Simplify: Substitute the expression for $ y $ from Step 2 into the first equation. Substituting $ y = 3 - x $ into $ x^2 + y^2 = 9 $ gives us: $ x^2 + (3 - x)^2 = 9 $Expand and Combine Terms: Expand the squared term and simplify the equation. Expanding $ (3 - x)^2 $ gives us $ 9 - 6x + x^2 $, so the equation becomes: $ x^2 + 9 - 6x + x^2 = 9 $ Combining like terms, we get: $ 2x^2 - 6x + 9 = 9 $Subtract to Simplify: Subtract 9 from both sides to simplify the equation further. $ 2x^2 - 6x + 9 - 9 = 9 - 9 $ This simplifies to: $ 2x^2 - 6x = 0 $Factor Out x: Factor out the common term $ x $. $ x(2x - 6) = 0 $Solve for x: Solve for $ x $ using the zero product property. Setting each factor equal to zero gives us two possible solutions for $ x $: 1) $ x = 0 $ 2) $ 2x - 6 = 0 $ which simplifies to $ x = 3 $Find y-Values: Find the corresponding $ y $-values for each $ x $-value. Using $ y = 3 - x $, we find the $ y $-values: For $ x = 0 $, $ y = 3 - 0 = 3 $ For $ x = 3 $, $ y = 3 - 3 = 0 $Calculate Product: Calculate the product of the $ y $-coordinates. The $ y $-coordinates are 3 and 0. The product of these is: $ 3 \times 0 = 0 $

If $(x,y)$ is a solution to the system of equations shown, what is the product of the y-coordinates of the solutions? $\newline$ $x^{2}+y^{2}=9$ $\newline$ $x+y=3$

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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-coordinates of the solutions?\newlinex2+y2=9x^{2}+y^{2}=9x2+y2=9 \newlinex+y=3 x+y=3x+y=3

If $(x,y)$ is a solution to the system of equations shown, what is the product of the y-coordinates of the solutions? $\newline$ $x^{2}+y^{2}=9$ $\newline$ $x+y=3$