Rewrite the equation 3x+y=7

Question

in slope-intercept form to select the statement that correctly describes the system of equations {3x+y=7
y=-3x+7

Statement #1: The system of equations has no solutions because the graphs of the two equations are parallel lines.

Statement #2: The system of equations has an infinite number of solutions because the graphs of the two equations occupy the same line.

(2 points)
The equation 3x+y=7
is y=

in slope intercept form, which means that statement #
describes the system of equations.

Answer 1

To rewrite the equation \( 3x + y = 7 \) in slope-intercept form (which is \( y = mx + b \)), we need to solve for \( y \):

1. Subtract \( 3x \) from both sides: \[ y = -3x + 7. \]

Now we can compare this with the second equation provided, \( y = -3x + 7 \).

Since both equations are identical, they represent the same line.

Thus, we can conclude:

The equation \( 3x + y = 7 \) is \( y = -3x + 7 \) in slope-intercept form, which means that statement #2 describes the system of equations, as the system has an infinite number of solutions because the graphs of the two equations occupy the same line.