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

Answer 1

To rewrite the equation \(3x + y = 7\) in slope-intercept form (which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept), we can follow these steps:

1. Subtract \(3x\) from both sides:

   \[ y = -3x + 7 \]

Now, the equation \(y = -3x + 7\) is in slope-intercept form.

To describe the system of equations, we need to know if there are other equations involved and their relationship (e.g., whether they are parallel, intersecting, or identical). If you have more equations to compare, please provide them, and I'll help you analyze the system!

Answer 2

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.
which statement describes the system of equations

Answer 3

To determine which statement describes the system of equations, we need to look at the rewritten equation \(y = -3x + 7\) and compare it to a second equation, if one exists.

• Statement #1: This statement implies that the second equation has the same slope but a different y-intercept. Since parallel lines never intersect, this means there would be no solutions for the system.

• Statement #2: This statement implies that the second equation is identical to the first one, meaning it has the same slope and y-intercept. If two lines are the same, they intersect at infinitely many points, resulting in an infinite number of solutions.

If the Second Equation is:

1. Parallel (e.g., \(y = -3x + 5\) or any equation with a slope of \(-3\) and a different y-intercept)

   • The correct statement would be Statement #1 (no solutions).

2. Identical (e.g., \(y = -3x + 7\) or any equivalent rearrangement of \(3x + y = 7\))

   • The correct statement would be Statement #2 (infinite solutions).

Please provide the second equation to accurately conclude which statement describes the system!