# Linear equations

Module 3 - Case

Systems of Linear Equations

Answer the question and solve the problems below. Make sure you show all your work so you can get partial credit even if you get the final answer wrong.

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.

#### Solution Preview

Systems of Linear Equations

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

3x - 2y = 6

2x + 3y = 6

NOTE: Compute for the values of x and y for each of the equation separately.

Example: 1st equation

3x - 2y = 6 , Let us extract the value of y;

When x = 0, what is the value of y? This can be computed in the following way:

3 (0) - 2y = 6

0 -2y = 6

-2y = 6

-2y = 6

---- -----

-2 -2

We can cancel out the -2 by -2. So the value of y becomes:

Y = 6/-2

y = -3

Using the same equation, Let us extract the value of x;

3x - 2y = 6

When y = 0, what is the value of x? This can be computed in the following way:

3x - 2y = 6

3x - 2(0) =6

3x = 6

3x = 6

---- -----

3 3

x = 6/3

x = 2

Example: 2nd equation

2x + 3y = 6 , Let us extract the value of y;

When x = 0, what is the value of y? This can be computed in the following way:

2x + 3y = 6

2 (0) + 3y = 6

0 + 3y = 6

3y = 6

y = 6/3

y = 2

When y = 0, what is the value of x? This can be computed in the following way:

2x + 3y = 6

2x + 3 (0) = 6

2x + 0 = 6

x = 6/2

x = 3

Summary:

For equation 3x - 2y = 6, the extracted values are

x = 2, y = -3

For equation 2x + 3y = 6, the extracted values are

x = 3, y = 2

(The plot the graph for the two equations is shown in ...

#### Solution Summary

This solution shows the step-by-step computation of linear equations.