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x-3y=8

y^(2)=x-4y-2
If 
(x,y) is a solution to the system of equations shown, which of the following are 
y-coordinates of the solutions?
Choose 1 answer:
(A) -1 and -3
(B) 14 and 2
(C) -2 and 3
(D) 2 and -3

x3y=8 x-3 y=8 \newliney2=x4y2 y^{2}=x-4 y-2 \newlineIf (x,y) (x, y) is a solution to the system of equations shown, which of the following are y y -coordinates of the solutions?\newlineChoose 11 answer:\newline(A) 1-1 and 3-3\newline(B) 1414 and 22\newline(C) 2-2 and 33\newline(D) 22 and 3-3

Full solution

Q. x3y=8 x-3 y=8 \newliney2=x4y2 y^{2}=x-4 y-2 \newlineIf (x,y) (x, y) is a solution to the system of equations shown, which of the following are y y -coordinates of the solutions?\newlineChoose 11 answer:\newline(A) 1-1 and 3-3\newline(B) 1414 and 22\newline(C) 2-2 and 33\newline(D) 22 and 3-3
  1. Solve for x: Solve the first equation for x.\newlineThe first equation is x3y=8x - 3y = 8. To solve for x, add 3y3y to both sides of the equation.\newlinex=3y+8x = 3y + 8
  2. Substitute into second equation: Substitute the expression for xx into the second equation.\newlineThe second equation is y2=x4y2y^2 = x - 4y - 2. Substitute xx with 3y+83y + 8.\newliney2=(3y+8)4y2y^2 = (3y + 8) - 4y - 2
  3. Simplify the equation: Simplify the equation.\newlineCombine like terms on the right side of the equation.\newliney2=3y+84y2y^2 = 3y + 8 - 4y - 2\newliney2=y+6y^2 = -y + 6
  4. Rearrange for quadratic equation: Rearrange the equation to form a quadratic equation.\newlineAdd yy to both sides and subtract 66 from both sides to set the equation to zero.\newliney2+y6=0y^2 + y - 6 = 0
  5. Factor the quadratic equation: Factor the quadratic equation.\newlineWe need to find two numbers that multiply to 6-6 and add up to 11. These numbers are 33 and 2-2.\newline(y+3)(y2)=0(y + 3)(y - 2) = 0
  6. Solve for y: Solve for y.\newlineSet each factor equal to zero and solve for y.\newliney+3=0y + 3 = 0 or y2=0y - 2 = 0\newliney=3y = -3 or y=2y = 2

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