# Solutions to Problem Set 7

Math 101-06

9-18-2017

[Lines]

1. Determine whether the following lines are parallel, perpendicular, or neither.

The slope of the line is .

The slope of the line is .

Since and are negative reciprocals, the lines are perpendicular.

2. Determine whether the following lines are parallel, perpendicular, or neither.

The slope of is -5.

The slope is -5.

Since both lines have slope -5, the lines are parallel.

3. Find the equation of the line which passes through the point and is parallel to the line .

The slope is -7.

A parallel line must also have slope -7. Using this slope and the point , the equation is

4. Find the equation of the line which passes through the point and is perpendicular to the line .

The slope is .

A perpendicular line must have slope . Using this slope and the point , the equation is

[Systems]

5. Solve the following system of equations for x and y.

Returning to the original equations, the coefficients of y are the same, but opposite in sign, so add the equations to eliminate y:

The solution is and .

6. Solve the following system of equations for x and y.

Returning to the original equations, multiply the first equation by 8, multiply the second equation by 3, then subtract the resulting equations:

The solution is and .

7. Solve the following system of equations for x and y.

Multiply the second equation by 7 and add the first equation:

The solution is and .

8. Solve the following system of equations for x and y.

The last equation is false. Therefore, the system has no solutions.

To think is not enough; you must think of something. - Jules Renard

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