Solve the system of equations:25+x2−10xy64+x2−16xy=16=(532)2
MathBot Answer:
The system of equations has 2 solutions.
x=−5610,y=−2003910x=5610,y=2003910
Solve x2−10xy+25=16 for x. x=5y−25y2−9,x=5y+25y2−9Substitute 5y−25y2−9 for x in x2−16xy+64=251024 and simplify. x2−16xy+64(5y−25y2−9)2−16(5y−25y2−9)y+64−30y2+6y25y2−9+55=251024=251024=251024Substitute −2003910 into x2−10xy+25=16 to solve for x. x2−10(−2003910)x+25x2+203910x+25x2+203910x+92020x2+3910x+180x=−5610=16=16=0=0,x=−4310This yields the following solution. x=−5610,y=−2003910Substitute 5y−25y2−9 for x in x2−16xy+64=251024 and simplify. x2−16xy+64(5y−25y2−9)2−16(5y−25y2−9)y+64−30y2+6y25y2−9+55=251024=251024=251024Substitute 5y+25y2−9 for x in x2−16xy+64=251024 and simplify. x2−16xy+64(5y+25y2−9)2−16(5y+25y2−9)y+6430y2+6y25y2−9−55=251024=251024=−251024Substitute 2003910 into x2−10xy+25=16 to solve for x. x2−10⋅2003910x+25x2−203910x+25x2−203910x+92020x2−3910x+180x=4310=16=16=0=0,x=5610This yields the following solution. x=5610,y=2003910