What is the solution of this system? 8x + 3y = -9 and -8x + y = 29

Graphing Linear Inequalities in One orTwo Variables

You graph inequalities the same way you graph lines (Just pretend the inequality sign is an equal sign, and graph the line) Changes with inequalities Lines are sometimes dashed and sometimes solid Shading needs to occur either above or below the line

If the sign is > or < the line will be dashed Graphing an Inequality in Two Variables If the sign is > or < the line will be dashed If the sign is  or  the line will be solid

When shading, as a general rule… If it is > or  then you shade above If it is < or  then you shade below the line However, we will always check our shading with an ordered pair, as you will see on the following examples

Picking points to help shade If you get confused where to shade, then you should always pick a point to check. If possible, use (0,0). You will always shade the TRUE side. So, when you put (0,0) into the inequality, if it makes the inequality TRUE, then that’s the side of the line that should be shaded. If (0,0) lies ON the line that you have graphed, then choose another ordered pair that is clearly on one side of the line. *see examples to make this more clear*

Graphing an Inequality in One Variable Graph x < 2 Step 1: Start by graphing the line x = 2 Make it dashed since there’s no equal sign Since it has to be x < 2 we shade everything to the left of the line. Pick (0,0) and see if it’s true… 0 < 2 TRUE! So we shaded correctly

Graphing an Inequality in One Variable Sketch a graph of y  3 Graph y = 3 Pick (0,0) again to see if you shaded correctly 0  3 FALSE! So you should have shaded away from (0,0), which you did! Solid line since there is an equal sign Shade above since you see the greater than symbol

Graphing an Inequality in Two Variables Sketch a graph of x + y < 3 Step 1: Put into slope intercept form y < -1x + 3 Step 2: Graph y = -1x + 3 Make it dashed since < Since it says <, shade below Pick an ordered pair like (0,0) to check our shading: 0 + 0 < 3 0 < 3 TRUE! So you should shade where (0,0) is located, which you did!

Graphing an Inequality in Two Variables Sketch a graph of 3x + 2y > 2 Step 1: Put into slope intercept form 2y > -3x + 2 y > -3/2x + 1 Step 2: Graph y = -3/2x + 1 Make dashed since > Since it says >, shade above Pick an ordered pair like (0,0) to check our shading: 3(0) + 2(0) > 2 0 > 2 FALSE! So you should shade where (0,0) is NOT, which you did!