Ask a New Question
Menu

Solve the following system of

linear equations by graphing.
Use your Desmos calculator to
graph them, and choose the
answer that matches the
solution.
y = 5x + 3
y = 5x + 15
(1 point)
No solutions
(3,5)
(5,3)
Infinite solutions

5 answers

To solve the system of equations by graphing, let's analyze the two equations given:

  1. \( y = 5x + 3 \)
  2. \( y = 5x + 15 \)

Both equations are in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

  • For the first equation \( y = 5x + 3 \), the slope is 5 and the y-intercept is 3.
  • For the second equation \( y = 5x + 15 \), the slope is also 5 but the y-intercept is 15.

Since both equations have the same slope (5), they are parallel lines. Parallel lines never intersect, which means there are no solutions to this system of equations.

Therefore, the answer to the problem is:

No solutions.

Yes, I am sure. Let's go through it one more time:

We have the following two equations:

  1. \( y = 5x + 3 \)
  2. \( y = 5x + 15 \)

Both equations are in slope-intercept form, which allows us to easily determine the relationships between them:

  • Both equations have the same slope of 5, which means they are parallel lines.
  • The y-intercept of the first equation is 3, and the y-intercept of the second equation is 15.

Since parallel lines do not intersect, they do not have any points in common. Hence, the system of equations has no solutions.

If you graph these equations on a graphing calculator like Desmos, you will see that the two lines are parallel and never meet, confirming that the solution is indeed no solutions.

this is last qeustion

I understand, and I appreciate your patience. To summarize and confirm the solution once more for clarity:

Given the equations:

  1. \( y = 5x + 3 \)
  2. \( y = 5x + 15 \)
  • Both lines have the same slope (5), indicating they are parallel.
  • The y-intercepts (3 for the first and 15 for the second) are different, which means they will never intersect.

Since parallel lines do not cross, there are no solutions to this system of equations.

If you're looking at options, the correct answer is indeed No solutions. If you graph these equations, you'll see that they do not touch each other at any point. If you have any further questions or need additional assistance, feel free to ask!