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Solving systems of linear equations: advanced

{:[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

Solving systems of linear equations: advanced $\newline$ $\begin{aligned} x-y & =y-4+2(4.5-2 x) \\ 4(x+2 y) & =-p+7 y \end{aligned}$ $\newline$ In the system of equations, $p$ is a constant. For which value of $p$ is there exactly one solution $(x, y)$ where $x=-1$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-5$ $\newline$ (B) $9$ $\newline$ (c) Any real number $\newline$ D) None of the above

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Compare linear and exponential growth

Full solution

Q. Solving systems of linear equations: advanced

\newline

\begin{aligned} x-y & =y-4+2(4.5-2 x) \\ 4(x+2 y) & =-p+7 y \end{aligned}

\newline

In the system of equations,

p

is a constant. For which value of

p

is there exactly one solution

(x, y)

where

x=-1

?

\newline

Choose

1

answer:

\newline

(A)

-5

\newline

(B)

9

\newline

(c) Any real number

\newline

D) None of the above

Substitute x = $-1$ : Substitute $x = -1$ into the first equation. $\newline$ $x - y = y - 4 + 2(4.5 - 2x)$ $\newline$ $-1 - y = y - 4 + 2(4.5 - 2(-1))$
Simplify the equation: $\newline$ Step $2$ : Simplify the equation. $\newline$ $-1 - y = y - 4 + 2(4.5 + 2)$ $\newline$ $-1 - y = y - 4 + 2(6.5)$ $\newline$ $-1 - y = y - 4 + 13$ $\newline$ $-1 - y = y + 9$
Solve for y: $\newline$ Step $3$ : Solve for $y$ . $\newline$ $-1 - y = y + 9$ $\newline$ $-1 - 9 = y + y$ $\newline$ $-10 = 2y$ $\newline$ $y = -5$
Substitute x = $-1$ and y = $-5$ : $\newline$ Step $4$ : Substitute $x = -1$ and $y = -5$ into the second equation. $\newline$ $4(x + 2y) = -p + 7y$ $\newline$ $4(-1 + 2(-5)) = -p + 7(-5)$ $\newline$ $4(-1 - 10) = -p - 35$ $\newline$ $4(-11) = -p - 35$ $\newline$ $-44 = -p - 35$
Solve for p: $\newline$ Step $5$ : Solve for $p$ . $\newline$ $-44 + 35 = -p$ $\newline$ $-9 = -p$ $\newline$ $p = 9$

More problems from Compare linear and exponential growth

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\newline

\newline

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\newline

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Posted 6 months ago

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Both of these functions grow as

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Question

f(x)

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are differentiable.

\newline

h(x)

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\newline

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h'(8)

\newline

Simplify any fractions.

\newline

h'(8)=

Posted 6 months ago

Question

p(x)

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are differentiable.

\newline

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r(x)= \frac{p(x)}{q(x)}

\newline

p(3)= 2

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\newline

Simplify any fractions.

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Posted 7 months ago

Question

u(x)

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are differentiable.

\newline

w(x)

w(x)= \frac{u(x)}{v(x)}

\newline

u(5)= 3

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\newline

Simplify any fractions.

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w'(5)=

Posted 7 months ago

Question

a(x)

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\newline

c(x)

c(x)= \frac{a(x)}{b(x)}

\newline

a(2)= 4

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b(2)= 1

b'(2)= -3

c'(2)

\newline

Simplify any fractions.

\newline

c'(2)=

Posted 7 months ago

Question

m(x)

n(x)

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\newline

o(x)

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\newline

m(7)= 2

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o'(7)

\newline

Simplify any fractions.

\newline

o'(7)=

Posted 7 months ago

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