{:[-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

Write Equations: First, let's write down the system of equations: 1. -6x + 4y = 2 2. 3x - 2y = -1Multiply Second Equation: Next, we'll multiply the second equation by 2 to align the coefficients of x for elimination: Original: 3x - 2y = -1 Multiplied by 2: 6x - 4y = -2Add Equations: Now, add the new equation from step 2 to the first equation: -6x + 4y = 2 + 6x - 4y = -2 ----------------- 0 = 0Check Solution: Since we ended up with a true statement (0=0) and no variables left, this indicates that the equations are dependent. This means there are 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 $\newline$

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Math Problems

Grade 8

Write an equation word problem

Full solution

\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

\newline

Write Equations: First, let's write down the system of equations: $\newline$ $1$ . $-6x + 4y = 2$ $\newline$ $2$ . $3x - 2y = -1$
Multiply Second Equation: Next, we'll multiply the second equation by $2$ to align the coefficients of $x$ for elimination: $\newline$ Original: $3x - 2y = -1$ $\newline$ Multiplied by $2$ : $6x - 4y = -2$
Add Equations: Now, add the new equation from step $2$ to the first equation: $\newline$ $-6x + 4y = 2$ $\newline$ $+ 6x - 4y = -2$ $\newline$ ----------------- $\newline$ $0 = 0$
Check Solution: Since we ended up with a true statement $0=0$ and no variables left, this indicates that the equations are dependent. This means there are infinitely many solutions.