SOLUTION: what are the solutions for 4x-5y=11 and x^2+y^2=25

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Question 908037: what are the solutions for 4x-5y=11 and x^2+y^2=25
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
4x-5y=11 and x^2+y^2=25
4x-5y=11
4x=5y+11
x=(5y+11)/4



and x^2+y^2=25
((5y+11)/4)^2+y^2= 25
(5y+11)^2/16 +y^2=25
multiply equation by 15
(5y+11)^2+16y^2=16*25
25y^2+110y+121+16y^2=400
41y^2+110y-279=0
Find the roots of the equation by quadratic formula

a= 41 , b= 110 , c= -279

b^2-4ac= 12100 + 45756
b^2-4ac= 57856
%09sqrt%28%0957856%09%29=%09240.53%09
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( -110 + 240.53 )/ 82
x1= 1.59
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( -110 -240.53 ) / 82
x2= -4.27

y=1.59 OR -4.27

when y = 1.59
4x-5y=11
4x-7.95=11
4x=18.95
x=4.73
One pair of solution is (4.73 & 1.59)
Other pair you can work out
using y=-4.27