How many solutions does the system of equations below have? {:[-10 x+3y=-8],[20 x-6y-16=0]:} (A) no solution (B) one solution (C) infinitely many solutions

Given Equations: We are given the system of equations: -10x + 3y = -8 20x - 6y = 16 First, let's simplify the second equation by dividing all terms by 2 to make it easier to compare with the first equation. 20x/2 - 6y/2 = 16/2 10x - 3y = 8Simplify Second Equation: Now we have the system of equations: -10x + 3y = -8 10x - 3y = 8 We can add the two equations together to see if they are consistent or inconsistent. (-10x + 3y) + (10x - 3y) = -8 + 8 -10x + 10x + 3y - 3y = 0 0 = 0Add Equations Together: Since the left-hand side of the equation simplifies to 0 and the right-hand side is also 0, the equations are dependent, meaning they represent the same line. Therefore, the system of equations has infinitely many solutions.

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How many solutions does the system of equations below have?
{:[-10 x+3y=-8],[20 x-6y-16=0]:}
(A) no solution
(B) one solution
(C) infinitely many solutions

How many solutions does the system of equations below have? $\newline$ $\begin{array}{l} -10 x+3 y=-8 \\ 20 x-6 y-16=0 \end{array}$ $\newline$ (A) no solution $\newline$ (B) one solution $\newline$ (C) infinitely many solutions

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Algebra 2

Determine the number of solutions to a system of equations in three variables

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Q. How many solutions does the system of equations below have?

\newline

\begin{array}{l} -10 x+3 y=-8 \\ 20 x-6 y-16=0 \end{array}

\newline

(A) no solution

\newline

(B) one solution

\newline

Given Equations: We are given the system of equations: $\newline$ $-10x + 3y = -8$ $\newline$ $20x - 6y = 16$ $\newline$ First, let's simplify the second equation by dividing all terms by $2$ to make it easier to compare with the first equation. $\newline$ $\frac{20x}{2} - \frac{6y}{2} = \frac{16}{2}$ $\newline$ $10x - 3y = 8$
Simplify Second Equation: Now we have the system of equations: $\newline$ $-10x + 3y = -8$ $\newline$ $10x - 3y = 8$ $\newline$ We can add the two equations together to see if they are consistent or inconsistent. $\newline$ $(-10x + 3y) + (10x - 3y) = -8 + 8$ $\newline$ $-10x + 10x + 3y - 3y = 0$ $\newline$ $0 = 0$
Add Equations Together: Since the left-hand side of the equation simplifies to $0$ and the right-hand side is also $0$ , the equations are dependent, meaning they represent the same line. $\newline$ Therefore, the system of equations has infinitely many solutions.