Question

page 16 of 16
Solving with Elimination Quick Check
2 of 52 of 5 Items


Question
How many solutions does the system of equations have?
8x−6y=48

8x+6y=48
(1 point)
Responses

infinite
infinite

none
none

one
one

two

Answer 1

To determine how many solutions the system of equations has, we need to analyze the equations:

1. \( 8x - 6y = 48 \)
2. \( 8x + 6y = 48 \)

We can rearrange these equations for better understanding.

From the first equation:
\[ 8x - 6y = 48 \]
can be rearranged to:
\[ 6y = 8x - 48 \]
or,
\[ y = \frac{4}{3}x - 8 \] (Equation 1)

From the second equation:
\[ 8x + 6y = 48 \]
can be rearranged to:
\[ 6y = 48 - 8x \]
or,
\[ y = -\frac{4}{3}x + 8 \] (Equation 2)

Now we can look at the slopes. The first equation has a slope of \( \frac{4}{3} \) and the second equation has a slope of \( -\frac{4}{3} \). Since the slopes are different, the lines represented by these equations will intersect at exactly one point.

Therefore, the system of equations has **one solution**.

The correct response is:
- **one**