19-38 y=76 x 24 x=-6(2y-1) Consider the system of equations. How many solutions (x,y) does this system have? Choose 1 answer: (A) 0 (B) Exactly 1 (C) Exactly 2 (D) Infinitely many

Simplify first equation: Simplify the first equation to find a relationship between x and y. The first equation is 19 - 38y = 76x. To simplify, we can divide both sides by 38 to isolate y in terms of x. y = (19 - 76x) / 38 y = 0.5 - 2xSimplify second equation: Simplify the second equation to find another relationship between x and y. The second equation is 24x = -6(2y - 1). We can distribute the -6 on the right side to simplify. 24x = -12y + 6 Now, we can isolate y in terms of x by adding 12y to both sides and then dividing by 12. 12y = 6 - 24x y = (6 - 24x) / 12 y = 0.5 - 2xCompare simplified equations: Compare the two simplified equations for y. Both equations after simplification give us y = 0.5 - 2x. This means that the two equations are actually the same line. Since both equations represent the same line, there are infinitely many points (x, y) that satisfy both equations.

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$19-38y=76x$ $\newline$ $24x=-6(2y-1)$ $\newline$ Consider the system of equations. How many solutions $(x,y)$ does this system have? $\newline$ Choose $1$ answer: $\newline$ (A) $0$ $\newline$ (B) Exactly $1$ $\newline$ (C) Exactly $2$ $\newline$ (D) Infinitely many

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19-38y=76x

\newline

24x=-6(2y-1)

\newline

Consider the system of equations. How many solutions

(x,y)

does this system have?

\newline

Choose

1

answer:

\newline

(A)

0

\newline

(B) Exactly

1

\newline

2

\newline

(D) Infinitely many

Simplify first equation: Simplify the first equation to find a relationship between $x$ and $y$ . The first equation is $19 - 38y = 76x$ . To simplify, we can divide both sides by $38$ to isolate $y$ in terms of $x$ . $y = \frac{19 - 76x}{38}$ $y = 0.5 - 2x$
Simplify second equation: Simplify the second equation to find another relationship between $x$ and $y$ . The second equation is $24x = -6(2y - 1)$ . We can distribute the $-6$ on the right side to simplify. $24x = -12y + 6$ Now, we can isolate $y$ in terms of $x$ by adding $12y$ to both sides and then dividing by $12$ . $12y = 6 - 24x$ $y$ $0$ $y$ $1$
Compare simplified equations: Compare the two simplified equations for $y$ . Both equations after simplification give us $y = 0.5 - 2x$ . This means that the two equations are actually the same line. Since both equations represent the same line, there are infinitely many points $(x, y)$ that satisfy both equations.