Math 3 Ch. 05.3 Systems Of Inequalities In Two Variables

Front 1

What is the general form of a system of linear inequalities in two variables?

Back 1

If A, B, and C are real numbers with A and B not both equal to zero, then:
Ax + By < C

Front 2

A linear inequality in two variables is simply:

Back 2

A linear equation in two variables with the equal sign replaced by an inequality symbol.

Front 3

The solution to an inequality is:

Back 3

an ordered pair

Front 4

An ordered pair satisfies the linear inequality in two variables: y > x - 3 whenever:

Back 4

the y-coordinate is greater than the x-coordinate minus 3

Front 5

What are the steps for solving a linear inequality in two variables?

Back 5

1) Change the inequality into an equation.
2) Solve for y in the new equation and graph it. If the inequality has an equal sign, graph a solid line, if not, graph a dotted line.
3) The graph obtained divides the plane into two half planes without including the line.
4) Pick a test point in one of the two planes and substitute its x and y values into the original inequality. If the inequality is satisfied, shade the test point region, if not, shade the other region.

Front 6

What are the steps for solving a system of linear inequalities in two variables?

Back 6

1) Change each equation and graph each one separately as usual using dotted lines.
2) Get test points on each plane around the intersection of the lines and check them in BOTH original inequalities.
3) Shade the plane in which the test points makes a true statement for BOTH inequalities, and make the line solid for each inequality that has an equals sign .