✒️Math

how did you determine the solution of each system of liner and qualitative and two variables by graphing

•••••••••••••••••••••••••••••••••••••••••••••••••

Graphing Systems of Linear Inequalities

To graph a linear inequality in two variables (say, xx and yy ), first get yy alone on one side. Then consider the related equation obtained by changing the inequality sign to an equality sign. The graph of this equation is a line.

If the inequality is strict ( << or >> ), graph a dashed line. If the inequality is not strict ( ≤≤ or ≥≥ ), graph a solid line.

Finally, pick one point that is not on either line ( (0,0)(0,0) is usually the easiest) and decide whether these coordinates satisfy the inequality or not. If they do, shade the half-plane containing that point. If they don't, shade the other half-plane.

Graph each of the inequalities in the system in a similar way. The solution of the system of inequalities is the intersection region of all the solutions in the system.

Example:

Solve the system of inequalities by graphing:

y ≤ x−2

y > −3x + 5

First, graph the inequality y ≤ x − 2 . The related equation is y = x − 2 .

Since the inequality is ≤ , not a strict one, the border line is solid.

Graph the straight line.

( Attached the Image 1st )

Consider a point that is not on the line - say, (0,0) - and substitute in the inequality

y ≤ x − 2 .

0 ≤ 0 − 2

0 ≤ − 2

This is false. So, the solution does not contain the point (0,0) . Shade the lower half of the line.

( Attached the Image 2nd )

Similarly, draw a dashed line for the related equation of the second inequality y > −3x + 5 which has a strict inequality. The point (0,0) does not satisfy the inequality, so shade the half that does not contain the point (0,0) .

( Attached the Image 3rd )

The solution of the system of inequalities is the intersection region of the solutions of the two inequalities.

( Attached the Image 4th )

᯽᯽᯽᯽᯽᯽᯽᯽᯽᯽᯽᯽᯽᯽᯽᯽

#BrainlyChallenge2021

#MerryChristmas

Please mark brainliest or thanks if it helped!