How many solutions does the system have? {[8x+2y=14],[8x+2y=4]:} Choose 1 answer: (A) Exactly one solution (B) No solutions (c) Infinitely many solutions

Analyze Equations: Let's analyze the system of equations: \[ \begin{cases} 8x + 2y = 14 \\ 8x + 2y = 4 \end{cases} \] We can see that both equations have the same coefficients for $x$ and $y$, but different constant terms. This suggests that the lines represented by these equations are parallel.Compare Slopes: To confirm if the lines are indeed parallel, we can compare the slopes of the lines. The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope. Let's convert the first equation to slope-intercept form by isolating $y$: \[ 8x + 2y = 14 \] \[ 2y = -8x + 14 \] \[ y = -4x + 7 \] The slope of the first line is $-4$.Convert to Slope-Intercept Form: Now, let's convert the second equation to slope-intercept form: \[ 8x + 2y = 4 \] \[ 2y = -8x + 4 \] \[ y = -4x + 2 \] The slope of the second line is also $-4$.Confirm Parallel Lines: Since both lines have the same slope but different $y$-intercepts ($7$ and $2$, respectively), they are parallel and will never intersect. Therefore, the system of equations has no solutions.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

How many solutions does the system have?

{[8x+2y=14],[8x+2y=4]:}
Choose 1 answer:
(A) Exactly one solution
(B) No solutions
(c) Infinitely many solutions

How many solutions does the system have? $\newline$ $\left\{\begin{array}{l} 8 x+2 y=14 \\ 8 x+2 y=4 \end{array}\right.$ $\newline$ Choose $1$ answer: $\newline$ (A) Exactly one solution $\newline$ (B) No solutions $\newline$ (C) Infinitely many solutions

View step-by-step help

Home

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} 8 x+2 y=14 \\ 8 x+2 y=4 \end{array}\right.

\newline

Choose

1

answer:

\newline

(A) Exactly one solution

\newline

(B) No solutions

\newline

Analyze Equations: Let's analyze the system of equations: $\newline$ $\begin{cases} 8x + 2y = 14 \\ 8x + 2y = 4 \end{cases}$ $\newline$ We can see that both equations have the same coefficients for $x$ and $y$ , but different constant terms. This suggests that the lines represented by these equations are parallel.
Compare Slopes: To confirm if the lines are indeed parallel, we can compare the slopes of the lines. The slope-intercept form of a line is $y = mx + b$ , where $m$ is the slope. Let's convert the first equation to slope-intercept form by isolating $y$ : $\newline$ $8x + 2y = 14$ $\newline$ $2y = -8x + 14$ $\newline$ $y = -4x + 7$ $\newline$ The slope of the first line is $-4$ .
Convert to Slope-Intercept Form: Now, let's convert the second equation to slope-intercept form: $\newline$ $8x + 2y = 4$ $\newline$ $2y = -8x + 4$ $\newline$ $y = -4x + 2$ $\newline$ The slope of the second line is also $-4$ .
Confirm Parallel Lines: Since both lines have the same slope but different $y$ -intercepts ( $7$ and $2$ , respectively), they are parallel and will never intersect. Therefore, the system of equations has no solutions.