How many solutions does the system of equations have?

Question

2x + 3y = 6

y = -2/3 x + 2

(1 point)
Responses

One Solution
One Solution

No Solution
No Solution

Two aolutions
Two aolutions

Infinite Solutions

Answer 1

To determine how many solutions the system of equations has, we can analyze both equations.

The first equation is: \[ 2x + 3y = 6 \]

The second equation is in slope-intercept form: \[ y = -\frac{2}{3}x + 2 \]

We can rewrite the first equation in slope-intercept form to compare slopes and intercepts:

1. Solve for \(y\) in the first equation: \[ 3y = 6 - 2x \] \[ y = -\frac{2}{3}x + 2 \]

Now we have both equations in the same format:

1. \( y = -\frac{2}{3}x + 2 \) (from the first equation)
2. \( y = -\frac{2}{3}x + 2 \) (as given in the second equation)

Both equations represent the same line. Since they are identical, we can conclude:

Infinite Solutions

So the answer is Infinite Solutions.