How can I solve the given simultaneous equation? I need help on two questions,can you teach me how solve it ?
1.
4x^2+2xy+x^2=25
y=2x
2.
b-2a=0
4a^2+2ab+a^2=25
Thanks in advance!
1.
4x^2+2xy+x^2=25
y=2x
2.
b-2a=0
4a^2+2ab+a^2=25
Thanks in advance!
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1.
4x^2+2xy+x^2=25
y=2x
Substitute y=2x in the first equation:
4x^2+2x(2x)+x^2=25
4x^2+4x^2+x^2=25
9x^2=25
9x^2-25=0
(3x+5)(3x-5)=0
i.e,3x+5=0==>3x=-5==>x=-5/3
or (3x-5)=0==>3x=5==>x=5/3
2.
b-2a=0==> b=2a
4a^2+2ab+a^2=25
Substitute b=2a in second equation:
4a^2+2a(2a)+a^2=25
4a^2+4a^2+a^2=25
9a^2=25
9a^2-25=0
(3a+5)(3a-5)=0
(3a+5)=0==>3a=-5==>a=-5/3
(3a-5)=0==>3a=5==>a=5/3
4x^2+2xy+x^2=25
y=2x
Substitute y=2x in the first equation:
4x^2+2x(2x)+x^2=25
4x^2+4x^2+x^2=25
9x^2=25
9x^2-25=0
(3x+5)(3x-5)=0
i.e,3x+5=0==>3x=-5==>x=-5/3
or (3x-5)=0==>3x=5==>x=5/3
2.
b-2a=0==> b=2a
4a^2+2ab+a^2=25
Substitute b=2a in second equation:
4a^2+2a(2a)+a^2=25
4a^2+4a^2+a^2=25
9a^2=25
9a^2-25=0
(3a+5)(3a-5)=0
(3a+5)=0==>3a=-5==>a=-5/3
(3a-5)=0==>3a=5==>a=5/3