Question

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

Answer 1

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=√(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\\ (1)/(2) \end{cases}\qquad y= \begin{cases} \boxed{1-x}\\ 2\\ (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=(4)/(3) \end{cases}\qquad x= \begin{cases} \boxed{2y}\\ 0\\ (8)/(3) \end{cases}`