{:[-6x+4y=2],[3x-2y=-1]:} Consider the system of equations. How many (x,y) solutions does this system have? Choose 1 answer: (A) No solutions (B) Exactly one solution (C) Exactly two solutions (D) Infinitely many solutions

Multiply by 2: First, let's multiply the second equation by 2 to make the coefficients of y the same. 2*(3x - 2y) = 2*(-1) 6x - 4y = -2Create new system: Now we have the system: {-6x + 4y = 2, 6x - 4y = -2}Eliminate y: Add the two equations together to eliminate y. (-6x + 4y) + (6x - 4y) = 2 + (-2) 0 = 0Infinitely many solutions: Since 0 = 0 is a true statement and we have eliminated both variables, this means the system has infinitely many solutions.

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{:[-6x+4y=2],[3x-2y=-1]:}
Consider the system of equations. How many
(x,y) solutions does this system have?
Choose 1 answer:
(A) No solutions
(B) Exactly one solution
(C) Exactly two solutions
(D) Infinitely many solutions

$\begin{aligned} -6 x+4 y & =2 \\ 3 x-2 y & =-1 \end{aligned}$ $\newline$ Consider the system of equations. How many $(x, y)$ solutions does this system have? $\newline$ Choose $1$ answer: $\newline$ (A) No solutions $\newline$ (B) Exactly one solution $\newline$ (C) Exactly two solutions $\newline$ D Infinitely many solutions

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Precalculus

Solve rational equations

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\begin{aligned} -6 x+4 y & =2 \\ 3 x-2 y & =-1 \end{aligned}

\newline

Consider the system of equations. How many

(x, y)

solutions does this system have?

\newline

Choose

1

answer:

\newline

(A) No solutions

\newline

(B) Exactly one solution

\newline

\newline

D Infinitely many solutions

Multiply by $2$ : First, let's multiply the second equation by $2$ to make the coefficients of $y$ the same. $\newline$ $2\times(3x - 2y) = 2\times(-1)$ $\newline$ $6x - 4y = -2$
Create new system: Now we have the system: $\{-6x + 4y = 2, 6x - 4y = -2\}$
Eliminate y: Add the two equations together to eliminate y. $\newline$ $(-6x + 4y) + (6x - 4y) = 2 + (-2)$ $\newline$ $0 = 0$
Infinitely many solutions: Since $0 = 0$ is a true statement and we have eliminated both variables, this means the system has infinitely many solutions.