Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.

Question

4, x, plus, 3, y, equals, minus, 8
4x+3y=
−8
minus, 8, x, minus, 6, y, equals, 16
−8x−6y=
16
Answer
Multiple Choice Answers
No SolutionsNo Solutions
One SolutionOne Solution
Infinitely Many SolutionsInfinitely Many Solutions

Answer 1

To determine if the system of equations has no solutions, infinitely many solutions, or exactly one solution, we can analyze the given equations.

The equations are:

1. \( 4x + 3y = -8 \)
2. \( -8x - 6y = 16 \)

First, let's rearrange the second equation for easier comparison:

The second equation can be simplified by dividing everything by -2:

\[ 4x + 3y = -8 \]

Now we see that both equations are actually the same:

1. \( 4x + 3y = -8 \)
2. \( 4x + 3y = -8 \)

Since both equations represent the same line, they have infinitely many solutions (any point on the line satisfies both equations).

Therefore, the answer is:

Infinitely Many Solutions