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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.

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

## Graphing and Solving Systems of Linear Equations

See attached file for full problem description.

Graph y = -1.

Solve the system by addition or substitution.
3x + 6y = 0
x =

Find the slope of the line passing through the points (-4, 10) and (-6, 5).

Solve: 6x + 4(3x - 2) = 6x + 2

Graph 3x + y = 3.

Let y vary directly with x, with a constant of variation k = 3.Graph the equation of variation.

Solve the system by substitution.
3x + 5y = 6
y = -x + 0

Find the slope and y-intercept.
6x + 5y = -35

Graph the solution set of x < 2.

Write the equation of the line that passes through point (0, -5) with a slope of 7.

Write the fraction in simplest form.

Write the equation of the line with x-intercept (-6, 0) and undefined slope.

Graph the inequality.
y > -5

Solve the system by graphing.
4x + 4y = 4
x + y = 1

Solve 10x-4-5x=6+3x-8

Given f(x) = -x3 - 3x2 + 3x + 3, find f(-3), f(0), and f(1)

Change the fraction to a decimal:

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