Page 751 - Algebra 1

Example
1
Solving by Graphing
Graph each system.
a. y>_1x-3 4
y ≤ 3x + 4. SOLUTION
Graph each inequality on the same plane. Every point in the overlapping region is a solution.
Check Substituteapointintheoverlappingregionto see that it satisfies both inequalities. The point (0, 0) is convenient to substitute.
y > _1 x - 3 y ≤ 3 x + 4 4
0> _1(0)-3 0≤3(0)+4 4
0>-3 ✓ 0≤4 ✓ b. y<4
2y + 2 > -6x.
SOLUTION
Write the second inequality in slope-intercept form.
2y + 2 > -6x
2y > -6x - 2
y > -3x - 1
Check See if (0, 0) satisfies both inequalities.
y < 4 2y + 2 > -6x
0 < 4 ✓ 2(0) + 2 > -6(0)
2>0 ✓
Solving with a Graphing Calculator
Graph the system on a graphing calculator.
y < _3 x + 2 4
y ≥ - _1 x + 4 5
SOLUTION Enter both functions. Use the arrow keys to move to the symbol to the left of Y1 and press enter until the symbol shows the lower half of a plane shaded. For Y2, select the symbol with the upper half shaded.
Note that for many graphing calculators, the option to choose between a strict and non-strict inequality does not exist.
Caution
Do not forget to use
a dashed line for the boundary line when the inequality has < or >.
O
-4
2
Example
2
736 Saxon Algebra 1
4
y
2
x
-2
4
-2
-4
y
2
x
-4
-2
2
4
-2
-4
Graphing Calculator Tip
For help with graphing inequalities, refer to
the graphing calculator keystrokes in Graphing Calculator Lab 9 on p. 645.