Y= 3x + 5 y = ax + b what values for a and b make the system inconsistent? what values for a and b make the system consistent and dependent? explain

3x+y=5
1x+y=1

y=3      x=1
 2x − y = 3 x + 3y = 5 

In this problem, we have the following linear equations:

We know that a linear equation is an equation for a line. In a system of linear equations, two or more equations work together.

1.  What values for a and b make the system inconsistent?

A system is inconsistent if and only if the lines are parallel in which case the system has no solution. This is illustrated in the first Figure bellow. Two lines are parallel if they share the same slope. So, the system is inconsistent for:

2. What values for a and b make the system consistent and dependent?

A system is consistent if and only if the lines are the same in which case the system has infinitely many solutions. This is illustrated in the second Figure bellow. So, the system is consistent and dependent for:

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Answercounterclockwise rotation about the origin by 180 degrees followed by reflection about the y-axisexplanationthe given figure has verticesrecall that for counterclockwise rotation about the origin, when we rotate figure pqrs counterclockwise through an angle of 180° about the origin, the coordinates will becomenext, we reflect in the y-axis by negating the x-coordinates of the resulting figure to obtain,therefore the correct answer is c