6x+2y=3 6x+y=3 Consider the given system of equations. How many (x,y) solutions does this system have? Choose 1 answer: (A) No solutions (B) Exactly one solution (C) Infinitely many solutions (D) None of the above

Analyze Equations: Analyze the given system of equations. We have two linear equations: 1) 6x + 2y = 3 2) 6x + y = 3 We will compare the coefficients of x and y in both equations to determine if they are parallel, the same line, or intersecting lines.Compare Equations: Compare the two equations. If we multiply the second equation by 2, we get: 2*(6x + y) = 2*3 Which simplifies to: 12x + 2y = 6 Now, we compare this with the first equation: 6x + 2y = 3 We can see that the coefficients of x and y are the same in both equations, but the constants on the right side are different. This means the lines are parallel and do not intersect.Conclude Solutions: Conclude the number of solutions. Since the lines are parallel and have different y-intercepts, they will never intersect. Therefore, there are no solutions to this system of equations.

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6x+2y=3

6x+y=3
Consider the given system of equations. How many
(x,y) solutions does this system have?
Choose 1 answer:
(A) No solutions
(B) Exactly one solution
(C) Infinitely many solutions
(D) None of the above

$6 x+2 y=3$ $\newline$ $6 x+y=3$ $\newline$ Consider the given 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) Infinitely many solutions $\newline$ (D) None of the above

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Full solution

6 x+2 y=3

\newline

6 x+y=3

\newline

Consider the given 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) None of the above

Analyze Equations: Analyze the given system of equations. $\newline$ We have two linear equations: $\newline$ $1$ ) $6x + 2y = 3$ $\newline$ $2$ ) $6x + y = 3$ $\newline$ We will compare the coefficients of $x$ and $y$ in both equations to determine if they are parallel, the same line, or intersecting lines.
Compare Equations: Compare the two equations. $\newline$ If we multiply the second equation by $2$ , we get: $\newline$ $2\times(6x + y) = 2\times3$ $\newline$ Which simplifies to: $\newline$ $12x + 2y = 6$ $\newline$ Now, we compare this with the first equation: $\newline$ $6x + 2y = 3$ $\newline$ We can see that the coefficients of $x$ and $y$ are the same in both equations, but the constants on the right side are different. This means the lines are parallel and do not intersect.
Conclude Solutions: Conclude the number of solutions. $\newline$ Since the lines are parallel and have different $y$ -intercepts, they will never intersect. Therefore, there are no solutions to this system of equations.