Question

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

Statement #1: The system of equations {3x+y=7y=−3x+7
{
3
𝑥
+
𝑦
=
7
𝑦
=
−
3
𝑥
+
7
has no solutions because the graphs of the two equations are parallel lines.

Statement #2: The system of equations {3x+y=7y=−3x+7
{
3
𝑥
+
𝑦
=
7
𝑦
=
−
3
𝑥
+
7
has an infinite number of solutions because the graphs of the two equations occupy the same line.

(1 point)
The equation 3x+y=7
3
𝑥
+
𝑦
=
7
is y=
𝑦
=
in slope-intercept form, which means that Statement describes the system of equations {3x+y=7y=−3x+7
{
3
𝑥
+
𝑦
=
7
𝑦
=
−
3
𝑥
+
7
.

Answer 1

Rewrite: 3x + y = 7 → y = −3x + 7.

Since the second equation is y = −3x + 7 as well, the two equations are identical (same slope and same y‑intercept), so Statement #2 is correct: the system has an infinite number of solutions.