1. Solve Systems of Equations & Graph Inequalities
Lesson 13.3 & 13.4

2. When two lines are graphed on the same coordinate plane, the lines may be:
Parallel
Intersecting
Identical (coincident)

3. Two methods to solve a system of Equations:
Substitution:
Substitute one equation into the other.
Find the intersection of the lines x = 4 and y = 2x + 8
Substitute 4: y = 2(4) + 8
y = 8 + 8
y = 16
The lines intersect at (4, 16)

4. Two methods to solve a system of Equations:
Linear Combinations:
Add the two equations together to cancel out one of the variables.
Find the intersection of the lines 8x – 3y = 7 and 10x + 4y = 1
Multiply the first equation by 4 and the second equation by 3.
32x – 12y = x + 12y = 3
62x = 31
x = ½
Substitute ½ into one of the equations for x and solve for y.
8(1/2) – 3y = 7
-3y = 3
y = -1
The lines intersect at (1/2 , -1)

5. Graph Inequalities
How to graph inequalities and system of inequalities:
Step 1: Pretend the inequality is an equation. Graph it the way you normally do. If the inequality is < or > use a dashed line. If it is ≤ or ≥ use a solid line.
Step 2: Use the inequality to test a point to find out which region to shade.

6. Graph y > 2x - 4
Graph the line as if it were an equation. Use a dashed line because it is >.
Use a test point to see where to shade.
0 > 2(0) – 4
0 > -4
True, shade where (0, 0) is.

7. Determine the solution set of the system by graphing:
y ≤ 2/5x + 4 y ≥ -½x x + y ≤ 8
Graph the 3 lines.
Test an ordered pair. (1, 4)
4 ≤ 2/5(1) ≤ 42/5 True
4 ≥ -½(1) ≥ 3½ True
2(1) + 4 ≤ 8 6 ≤ 8 True
Shade where (1, 4) is.