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.

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 can isolate \(y\):

1. Start with the original equation: \[3x + y = 7\]

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

Now we have \(y = -3x + 7\) in slope-intercept form.

Since both the original equation and the transformed equation represent the same line, the correct statement is:

The equation \(3x+y=7\) is \(y = -3x + 7\) in slope-intercept form, which means that statement #2 describes the system of equations.