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{:[x-y=y-4+2(4.5-2x)],[4(x+2y)=-p+7y]:}
In the system of equations, 
p is a constant. For which value of 
p is there exactly one solution 
(x,y) where 
x=-1 ?
Choose 1 answer:
(A) -5
(B) 9
(C) Any real number
(D) None of the above

xyamp;=y4+2(4.52x)4(x+2y)amp;=p+7y \begin{aligned} x-y & =y-4+2(4.5-2 x) \\ 4(x+2 y) & =-p+7 y \end{aligned} \newlineIn the system of equations, p p is a constant. For which value of p p is there exactly one solution (x,y) (x, y) where x=1 x=-1 ?\newlineChoose 11 answer:\newline(A) 5-5\newline(B) 99\newline(C) Any real number\newline(D) None of the above

Full solution

Q. xy=y4+2(4.52x)4(x+2y)=p+7y \begin{aligned} x-y & =y-4+2(4.5-2 x) \\ 4(x+2 y) & =-p+7 y \end{aligned} \newlineIn the system of equations, p p is a constant. For which value of p p is there exactly one solution (x,y) (x, y) where x=1 x=-1 ?\newlineChoose 11 answer:\newline(A) 5-5\newline(B) 99\newline(C) Any real number\newline(D) None of the above
  1. Substitute x=1x = -1: Substitute x=1x = -1 into the first equation xy=y4+2(4.52x)x - y = y - 4 + 2(4.5 - 2x).\newlineThis gives us 1y=y4+2(4.52(1))-1 - y = y - 4 + 2(4.5 - 2(-1)).
  2. Simplify to find yy: Simplify the equation to find yy.1y=y4+9+4-1 - y = y - 4 + 9 + 4. This simplifies to 1y=y+9-1 - y = y + 9.
  3. Combine terms to solve: Combine like terms to solve for yy.1yy=9-1 - y - y = 9. This simplifies to 12y=9-1 - 2y = 9.
  4. Add 11 to isolate: Add 11 to both sides to isolate the term with yy.\newline2y=10-2y = 10.
  5. Divide to find yy: Divide both sides by 2-2 to solve for yy.y=5.y = -5.
  6. Substitute x,yx,y into second: Now substitute x=1x = -1 and y=5y = -5 into the second equation 4(x+2y)=p+7y4(x + 2y) = -p + 7y. This gives us 4(1+2(5))=p+7(5)4(-1 + 2(-5)) = -p + 7(-5).
  7. Simplify to find pp: Simplify the equation to find pp.4(110)=p354(-1 - 10) = -p - 35.This simplifies to 44=p35-44 = -p - 35.
  8. Add 3535 to solve: Add 3535 to both sides to solve for pp.44+35=p-44 + 35 = -p.This simplifies to 9=p-9 = -p.
  9. Multiply to find pp: Multiply both sides by 1-1 to solve for pp.p=9.p = 9.

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