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{:[-x+3=y],[-6x+18=6y]:}
Which of the following accurately describes all solutions to the system of equations shown?
Choose 1 answer:
A
x=0 and
y=3
(B)
x=3 and
y=0
(c) There are infinite solutions to the system.
(D) There are no solutions to the system.

$\begin{array}{c} -x+3=y \\ -6 x+18=6 y \end{array}$ $\newline$ Which of the following accurately describes all solutions to the system of equations shown? $\newline$ Choose $1$ answer: $\newline$ (A) $x=0$ and $y=3$ $\newline$ (B) $x=3$ and $y=0$ $\newline$ (C) There are infinite solutions to the system. $\newline$ D There are no solutions to the system.

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Solve rational equations

Full solution

Q.

\begin{array}{c} -x+3=y \\ -6 x+18=6 y \end{array}

\newline

Which of the following accurately describes all solutions to the system of equations shown?

\newline

Choose

1

answer:

\newline

(A)

x=0

and

y=3

\newline

(B)

x=3

and

y=0

\newline

(C) There are infinite solutions to the system.

\newline

D There are no solutions to the system.

Analyze Equations: Let's analyze the system of equations given: $\newline$ $\begin{align*} -x + 3 &= y \quad \text{(Equation 1)} \\ -6x + 18 &= 6y \quad \text{(Equation 2)} \end{align*}$ $\newline$ We will try to solve this system by comparing the two equations.
Simplify Equation $2$ : First, we can simplify Equation $2$ by dividing every term by $6$ to see if it matches Equation $1$ : $\newline$ $\frac{-6x}{6} + \frac{18}{6} = \frac{6y}{6}$ $\newline$ This simplifies to: $\newline$ $-x + 3 = y$
Identical Equations: We notice that after simplifying Equation $2$ , it becomes identical to Equation $1$ : $\newline$ $-x + 3 = y$ $\newline$ This means that both equations represent the same line.
Infinite Solutions: Since both equations represent the same line, every point on the line is a solution to the system. Therefore, there are infinitely many solutions to the system.

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