### 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.)
- 2 x + 3 y = 4,

5 x - 2 y = 9

- x + y = 4,

2 x - 3 y = 6

- 3 x + 9 y + 12 z = 45,

-4 x - 9 y - 10 z = -36,

-2 x - 2 y - z = -4

- 5 x - 5 y - 5 z = 40,

-2 x - 6 z = -20,

x - 4 y - 8 z = 7

- 2 x + 4 y + 6 z = 4,

x + 5 y + 9 z = 2,

2 x + y + 3 z = 7

- 4 x + 8 y + 4 z = 80,

2 x + y - 4 z = 7,

3 x - y + 2 z = 22

- 2 x - 2 y + 4 z = 22,

-3 x + 6 y - 18 z = -102,

-3 x + 4 y - 12 z = -66

- 3 x + 2 y + z = 14,

2 x + y + 2 z = 10,

-3 x + 4 y + 3 z = 2

- a - 3 b + 2 c + 4 d = 6,

5 c + 5 d = 7,

5 d = 8

- 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