How many solutions does the system have? {[y=-2x+4],[7y=-14 x+28]:} Choose 1 answer: (A) Exactly one solution (B) No solutions (C) Infinitely many solutions

Analyze first equation: Let's analyze the first equation: y = -2x + 4 This is a linear equation in slope-intercept form, where the slope is -2 and the y-intercept is 4.Analyze second equation: Now let's analyze the second equation: 7y = -14x + 28 To compare it with the first equation, we should write it in slope-intercept form by dividing every term by 7: y = (-14/7)x + (28/7) y = -2x + 4Compare slopes and y-intercepts: We have: First equation: y = -2x + 4 Second equation: y = -2x + 4 Let's compare the slopes and y-intercepts of both equations. Slope of the first equation: -2 Slope of the second equation: -2 Y-intercept of the first equation: 4 Y-intercept of the second equation: 4Determine the number of solutions: Since both equations have the same slope and the same y-intercept, they represent the same line. Therefore, the system of equations has infinitely many solutions because every point on the line is a solution to both equations.

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How many solutions does the system have?

{[y=-2x+4],[7y=-14 x+28]:}
Choose 1 answer:
(A) Exactly one solution
(B) No solutions
(C) Infinitely many solutions

How many solutions does the system have? $\newline$ $\left\{\begin{array}{l} y=-2 x+4 \\ 7 y=-14 x+28 \end{array}\right.$ $\newline$ Choose $1$ answer: $\newline$ (A) Exactly one solution $\newline$ (B) No solutions $\newline$ (C) Infinitely many solutions

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Math Problems

Algebra 2

Find the number of solutions to a system of equations

Full solution

Q. How many solutions does the system have?

\newline

\left\{\begin{array}{l} y=-2 x+4 \\ 7 y=-14 x+28 \end{array}\right.

\newline

Choose

1

answer:

\newline

(A) Exactly one solution

\newline

(B) No solutions

\newline

Analyze first equation: Let's analyze the first equation: $\newline$ y = $-2$ x + $4$ $\newline$ This is a linear equation in slope-intercept form, where the slope is $-2$ and the y-intercept is $4$ .
Analyze second equation: Now let's analyze the second equation: $\newline$ $7y = -14x + 28$ $\newline$ To compare it with the first equation, we should write it in slope-intercept form by dividing every term by $7$ : $\newline$ $y = \left(-\frac{14}{7}\right)x + \left(\frac{28}{7}\right)$ $\newline$ $y = -2x + 4$
Compare slopes and y-intercepts: We have: $\newline$ First equation: $y = -2x + 4$ $\newline$ Second equation: $y = -2x + 4$ $\newline$ Let's compare the slopes and y-intercepts of both equations. $\newline$ Slope of the first equation: $-2$ $\newline$ Slope of the second equation: $-2$ $\newline$ Y-intercept of the first equation: $4$ $\newline$ Y-intercept of the second equation: $4$
Determine the number of solutions: Since both equations have the same slope and the same $y$ -intercept, they represent the same line. $\newline$ Therefore, the system of equations has infinitely many solutions because every point on the line is a solution to both equations.