Question

A system of linear equations is shown.
3x-4y = -10
3x - 4y = -24
What is the solution to the system of equations?
a.No Solution
b.(4,9)
c.(2.4)
d.(-2,1)

Answer 1

To determine the solution to the system of equations, we can analyze the two equations provided:

1. \( 3x - 4y = -10 \)
2. \( 3x - 4y = -24 \)

Notice that both equations left-hand sides (\(3x - 4y\)) are the same. This indicates that they're parallel lines since the coefficients of \(x\) and \(y\) are identical.

Now, let's examine the right-hand sides of the equations:

- The first equation equals \(-10\).
- The second equation equals \(-24\).

Since the left sides are identical and the right sides are different, this means the two lines represented by these equations will never intersect. Therefore, there is no solution to this system of equations.

The correct answer is:
a. No Solution