### Chapter 7 - Algebra Coach Exercises

Algebra Coach Exercise on systems of equations.
Solve each of the following systems of equations by both the method of elimination and the method of substitution. To do this drag-and-drop each of them into the Algebra Coach and click either the Solve by Elimination button or the Solve by Substitution button. (Click here for instructions on using the Algebra Coach to solve systems of equations by elimination and click here for instructions on solving by substitution.)
1. 2 x + 3 y = 4,
5 x - 2 y = 9

2. x + y = 4,
2 x - 3 y = 6

3. 3 x + 9 y + 12 z = 45,
-4 x - 9 y - 10 z = -36,
-2 x - 2 y - z = -4

4. 5 x - 5 y - 5 z = 40,
-2 x - 6 z = -20,
x - 4 y - 8 z = 7

5. 2 x + 4 y + 6 z = 4,
x + 5 y + 9 z = 2,
2 x + y + 3 z = 7

6. 4 x + 8 y + 4 z = 80,
2 x + y - 4 z = 7,
3 x - y + 2 z = 22

7. 2 x - 2 y + 4 z = 22,
-3 x + 6 y - 18 z = -102,
-3 x + 4 y - 12 z = -66

8. 3 x + 2 y + z = 14,
2 x + y + 2 z = 10,
-3 x + 4 y + 3 z = 2

9. a - 3 b + 2 c + 4 d = 6,
5 c + 5 d = 7,
5 d = 8

10. x + 2 y - 7 z + 5 w = 4,
3 x + 5 y + 9 z - 6 w = -8,
3 x - 6 y - 4 z + 9 w = 23,
45 x + 76 y + 6 z + 4 w = -55