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system of linear equation and compound inequality

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Please see attached file for full problem description.

Solve system by the substitution method.

1. y = 2x - 6
y = x - 5

2. 7x - 4y = 26
y = x - 5

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Solve each system by the addition method. If there is no solution or an infinite number of solutions, so state.
3.6x + 2y = 8
2x - y = 6

4. 7x - 2y = 8
-14x + 4y = 8

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5. Solve the compound inequality. Give the graph or describe it.
x < 5 and x > 4

Solve each absolute value equation or inequality

6.|x - 5 | > -1

Solve the inequality:

7. 3 | 2x +3 | + 6 > 0

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It shows how to solve the system of linear equation and compound inequality, respectively. The solution is detailed and was rated '5/5' by the student who posted the questions originally.

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Solve system by the substitution method.

1. y = 2x - 6 (1)
y = x - 5 (2)
Substitute (2) to (1):

Move x terms to the left side,

Then y =x - 5 = 1 - 5 = - 4.
Solution: x = 1, y = - 4, (1, -4)

2. 7x - 4y = 26 (1)
y = x - 5 (2)
(2) to (1):

Then y = x - 5 = 2 - 5 = ...

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