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: First, let's simplify each equation to see if we can find a relationship between x and y. Starting with the first equation: 19 - 38y = 76x We can divide both sides by 19 to simplify: 1 - 2y = 4x Now, let's isolate y: 2y = 1 - 4x y = (1 - 4x) / 2Isolate y in first equation: Next, let's simplify the second equation: 24x = -6(2y - 1) We can distribute the -6: 24x = -12y + 6 Now, let's isolate y: -12y = 24x - 6 y = (6 - 24x) / -12 y = -1/2 + 2xSimplify second equation: Now we have two expressions for y: y = (1 - 4x) / 2 y = -1/2 + 2x Let's set them equal to each other to see if there is a solution for x that satisfies both equations: (1 - 4x) / 2 = -1/2 + 2xIsolate y in second equation: To solve for x, we can multiply both sides by 2 to get rid of the denominators: 1 - 4x = -1 + 4x Now, let's add 4x to both sides: 1 = -1 + 8x Then, add 1 to both sides: 2 = 8x Now, divide both sides by 8: x = 2 / 8 x = 1 / 4Set equations equal to each other: Now that we have the value for x, let's substitute it back into one of the expressions for y to find the corresponding y value: y = (1 - 4(1/4)) / 2 y = (1 - 1) / 2 y = 0 / 2 y = 0

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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

$19-38 y=76 x$ $\newline$ $24 x=-6(2 y-1)$ $\newline$ 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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Math Problems

Algebra 1

Find the number of solutions to a system of equations

Full solution

19-38 y=76 x

\newline

24 x=-6(2 y-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: First, let's simplify each equation to see if we can find a relationship between $x$ and $y$ . Starting with the first equation: $19 - 38y = 76x$ We can divide both sides by $19$ to simplify: $1 - 2y = 4x$ Now, let's isolate $y$ : $2y = 1 - 4x$ $y = \frac{1 - 4x}{2}$
Isolate $y$ in first equation: Next, let's simplify the second equation: $\newline$ $24x = -6(2y - 1)$ $\newline$ We can distribute the $-6$ : $\newline$ $24x = -12y + 6$ $\newline$ Now, let's isolate $y$ : $\newline$ $-12y = 24x - 6$ $\newline$ $y = (6 - 24x) / -12$ $\newline$ $y = -1/2 + 2x$
Simplify second equation: Now we have two expressions for $y$ : $y = \frac{1 - 4x}{2}$ $y = -\frac{1}{2} + 2x$ Let's set them equal to each other to see if there is a solution for $x$ that satisfies both equations: $\frac{1 - 4x}{2} = -\frac{1}{2} + 2x$
Isolate y in second equation: To solve for x, we can multiply both sides by $2$ to get rid of the denominators: $\newline$ $1 - 4x = -1 + 4x$ $\newline$ Now, let's add $4$ x to both sides: $\newline$ $1 = -1 + 8x$ $\newline$ Then, add $1$ to both sides: $\newline$ $2 = 8x$ $\newline$ Now, divide both sides by $8$ : $\newline$ $x = \frac{2}{8}$ $\newline$ $x = \frac{1}{4}$
Set equations equal to each other: Now that we have the value for $x$ , let's substitute it back into one of the expressions for $y$ to find the corresponding $y$ value: $\newline$ $y = \frac{1 - 4(\frac{1}{4})}{2}$ $\newline$ $y = \frac{1 - 1}{2}$ $\newline$ $y = \frac{0}{2}$ $\newline$ $y = 0$