Reese states that the system of equations has no solution because the slopes are the same. Describe Reese’s error. ( y=−3x−1 ), ( 3+y=−1 )

the system of equations has infinite solution

Step-by-step explanation:

Reese states that the system of equations has no solution because the slopes are the same. Describe Reese’s error. ( y=−3x−1 ), ( 3x+y=−1 )

Solution:

The equation of a straight line graph is given by:

y = mx + b, where m is the slope of the line and b is the y intercept.

A system of linear equations has no solution when the graphs are parallel, that is they have the same slope and different y intercept.

A system of linear equations has infinite solutions when the graphs are the exact same line, that is they have the equal slope and equal y intercept.

The first equation: y = -3x - 1 has a slope of -3 and y intercept of -1.

The second equation: 3x + y = - 1; i.e. y = -3x - 1  has a slope of -3 and y intercept of -1.

Since both equations have equal slope and equal y intercept, hence both equations are infinite solutions.

Therefore the statement that the system of equations has no solution is wrong.