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Help Me Please!!

 

System of Equation: solve the system and express answers as ordered pairs

 

{x2+y2=34

{x+y=8

ManuelBautista2019  Mar 8, 2018
 #1
avatar+20537 
+1

Help Me Please!!

System of Equation: solve the system and express answers as ordered pairs

{x2+y2=34}

{x+y=8}

 

\(\begin{array}{|rclrcl|} \hline x^2+y^2 &=& 34 & x + y &=& 8 \\ && & y &=& 8 -x \\\\ x^2 +(8-x)^2 &=& 34 \\ x^2 + 64-16x+x^2 &=& 34 \\ 2x^2 -16x + 64-34 &=& 0 \\ 2x^2 -16x + 30 &=& 0 \quad & | \quad :2 \\ x^2 -8x + 15 &=& 0 \\\\ x_{1,2} &=& \dfrac{8 \pm \sqrt{64-4\cdot 15} }{2} \\\\ &=& \dfrac{8 \pm \sqrt{4} }{2} \\\\ &=& \dfrac{8 \pm 2 }{2} \\\\ &=& 4\pm 1 \\\\ x_1 &=& 4+1 = 5 \\ x_2 &=& 4-1 = 3 \\\\ y_1 &=& 8-x_1 =8-5 = 3 \\ y_2 &=& 8-x_2= 8-3 = 5 \\ \hline \end{array}\)

 

\(x_1 = 5 \qquad x_2 = 3 \\ y_1 = 3 \qquad y_2 = 5 \)

 

 

laugh

heureka  Mar 8, 2018
edited by heureka  Mar 8, 2018
 #2
avatar+1318 
+1

wow..thanks Heureka

ManuelBautista2019  Mar 8, 2018

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