1. Solving Systems Using Elimination
Chapter 7 Section 3
Solving Systems Using Elimination

2. When both equations are in Ax + By = C form you can solve by using elimination
*make sure both equations are in Ax + By = C form
Steps
Make either the x or y term additive inverses, if
necessary
Combine the 2 equations
Solve for the variable that remains
Pick one equation
Substitute the value of the variable you solved for
Find the value of the 2nd variable

3. *make sure both equations are in Ax + By = C form
Example 1
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6 √
5x – 6y = -32
3x + 6y = 48
8x = 16
x = 2
5x – 6y = -32
5(2) – 6y = -32
10 – 6y = -32
–10 –10
-6y = -42
y = 7
The solution is (2,7)

4. The solution is (89,203), 89 adult, and 203 student
Example 2
Suppose your community center sells a total of 292 tickets for a basketball game. An adult ticket costs $3. A student ticket costs $1. The sponsors collect $470 in ticket sales. Write and solve a system to find the number of each type of ticket sold.
a + s = 292
3a + s = 470
-1(a + s = 292)
-a – s = -292
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6 √
-a – s = -292
3a + s = 470
2a = 178
a = 89
a + s = 292
89 + s = 292
– –89
s = 203
The solution is (89,203), 89 adult, and 203 student

5. The solution is (-4,-1/2) Example 3 9a = 72b –72b –72b 9a – 72b = 0
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6 √
9(-5a + 14b = 13)
5(9a – 72b = 0)
-5a + 14b = 13
9a – 72b = 0
9a = 72b
9a = 72 (-1/2)
9a = -36
a = -4
-45a + 126b = 117
45a – 360b = 0
-234b = 117
b = -1/2
The solution is (-4,-1/2)

6. Questions?
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7. Assignments
Class Work
Page 390 – 392 #1 – 16, 17 – 37 odd
Homework
Finish Class Work; Page 393 #51 – 56