Equations of Lines and Solving Systems of Linear Equations ( Simultaneous Equations )

1. Find the slope of the line that passes through the points (2, 3) and (5, 8).

2. Find the equation of the line that passes through the points (3, -2) and (4, -2).

3. Find the equation, in standard form, with all integer coefficients, of the line perpendicular to x + 3y = 6 and passing through (-3, 5).

4. Solve the system of equations using the substitution method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is "no solution" or "infinitely many solutions."
-3x + y = 1
5x + 2y = -4

5. Solve the system of equations using the addition (elimination) method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is "no solution" or "infinitely many solutions."
-7x + y = 8
2x - y = 2

6. Solve the system of equations using the addition (elimination) method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is "no solution" or "infinitely many solutions."
3x - 2y = -7
-9x + 6y = 21

Equations of Lines and Solving Systems of Linear Equations are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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