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# Systems of Linear Equations - Graphs

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Answer the question and solve the problems below. Make sure you show all your work.

1. Determine whether the lines will be perpendicular when graphed.

3x - 2y = 6
2x + 3y = 6

2. Alice's Restaurant has a total of 205 seats. The number of seats in the non-smoking section is 73 more than twice the number of seats in the smoking section. How many seats are in each section?

3. Solve the system of equations by the substitution method

x + 3y = 32
-3x + 2y = 3

4. Solve the system of equations

x + y = 5
x - y = -9

5. Ricks Paint Store sells a special shade of pink paint (Ricky's Blush) which can be made from red paint and white paint. The amount of red paint should be three times the amount of white paint. How much of each kind of paint is needed to make 264 gallons of Ricky's Blush?

Assignment Expectations:

Define a system of equations.
Solve systems of equations with two and three variables.

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https://brainmass.com/math/linear-algebra/390070

#### Solution Preview

3x - 2y = 6

2x + 3y = 6

The slope-intercept form of the equations are:

Y = 3/2x - 3
Y = -2/3x + 2

Since the slopes are 3/2 and -2/3, the lines are perpendicular.

Alice's Restaurant has a total of 205 ...

\$2.19