I already asked this but could you please help me on E F G H four questions on stimultaneous equations. There is also an attachment. ASAP Thank You So Much

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jdoe0001

I already asked this but could you please help me on E F G H four questions on stimultaneous equations. There is also an attachment.

ASAP Thank You So Much

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(Based on todays review)

jdoe0001

E)

$\bf \begin{cases}
x^2-2xy-y^2=7\\
x+y=1\implies \boxed{y=1-x}
\end{cases}
\\\\\\
x^2-2x(1-x)-(1-x)^2=7
\\\\\\
x^2-2x+2x^2-(1-2x+x^2)=7
\\\\\\
\underline{x^2-2x}+2x^2-1\underline{+2x-x^2}=7\implies 2x^2-1-7
\\\\\\
2x^2=8\implies x^2=\cfrac{8}{2}\implies x^2=4\implies x=\sqrt{4}\implies
\begin{cases}
x=2\\
-----\\
\boxed{y=1-x}\\
y=-1
\end{cases}$

f)

$\bf \begin{cases}
3x^2-x-y^2=0\\
x+y-1=0\implies \boxed{y=1-x}
\end{cases}
\\\\\\
3x^2-x-(1-x)^2=0\implies 3x^2-x-(1-2x+x^2)=0
\\\\\\
3x^2-x-1+2x-x^2=0\implies 2x^2+x-1=0
\\\\\\
(2x-1)(x+1)=0\implies x=
\begin{cases}
-1\\
\frac{1}{2}
\end{cases}\qquad y=
\begin{cases}
\boxed{1-x}\\
2\\
\frac{1}{2}
\end{cases}$

g)

$\bf \begin{cases}
2x^2+xy+y^2=22\\
x+y=4\implies \boxed{y=4-x}
\end{cases}
\\\\\\
2x^2+x(4-x)+(4-x)^2=22
\\\\\\
2x^2+4x\underline{-x^2}+16-8x\underline{+x^2}=22\implies 2x^2-4x+16=22
\\\\\\
2x^2-4x-6=0\implies x^2-2x-3=0
\\\\\\
(x-3)(x+1)=0\implies x=
\begin{cases}
-1\\
3
\end{cases}\qquad y=
\begin{cases}
\boxed{4-x}\\
5\\
1
\end{cases}$

h)

$\bf \begin{cases}
x^2-4y-y^2=0\\
x-2y=0\implies \boxed{x=2y}
\end{cases}
\\\\\\
(2y)^2-4y-y^2=0\implies 4y^2-4y-y^2=0\implies 3y^2-4y=0
\\\\\\
y(3y-4)=0\implies 
\begin{cases}
y=0\\
-----\\
3y-4=0\\
3y=4\\
y=\frac{4}{3}
\end{cases}\qquad x=
\begin{cases}
\boxed{2y}\\
0\\
\frac{8}{3}
\end{cases}$
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