1. Which x-values should I choose to graph these equations (y = x; y = -x + 6) so that they intersect?

2. The school band sells carnations on Valentine's Day for $2 each. They buy the carnations from a florist for $0.50 each, plus a $16 delivery charge.

a. Write a system of equations to describe the situation.

b. Graph the system. What does the solution represent?

c. Explain whether the solution shown on the graph makes sense in this situation. If not, give a reasonable solution.

3. -x/5 = 12
A: x = -60?

4. 2/5 = y/12
A: 30 = y?

5. 6(x + 2) = -2(x + 10)
A: x = -8?

6. 4 (2x + 1) > 28
A: x > 3?

7. 1/8x + 3/5 <= 3/8
A: ?

1) (3,3)

2) y = 2x
y = .50x + 16

3) -x/5 = 12

X = -60
Vertical line so slope is undefined
4. 2/5 = y/12

y = 12(2/5) = 24/5
y = 24/5
Horizontal line so slope is 0

5) 6x + 12 = -2x -20
8x = -32
x = -4
6) 8x + 4 > 28
8x > 24
x > 3

7) 5x + 24 <= 15
5x >= -9
x <= -9/5

I usually pick values of x near the origin of the x-y grid

e.g. x = 0 , ± 1, ± 2 , ±3

since you know it is a straight line, you really only need 2 points.
But, I usually take a third point as a check:
x=0 , y1 - 0 , y2 = 6
x = 1 y1 = 1 , y2 = -1+6 = 5
x = 4, y1 = 4, y2 = -4+6 = 2

so I got 3 points for each of the lines
line1 -- (0,0), (1,1) , (4,4)
line2 -- (0,6) , (1 , 5) and (4,2)

notice had I picked x = 3
line1 : point (3,3)
line 2 : point is (3,3) , well , what do you know ?!

2 a) Don't know what you mean by the "situation"
Was there a situation for him to buy roses for Valentines ?
Where does the delivery charge come in ?
In the selling of them or when they bought tem?

#3 good
#4 good

#5
6x + 12 = -2x - 20
8x = -32
x= -4

#6 good

#7
multiply each term by 40 , the LCD, to clear the fractions
5x + 24 ≤ 15
5x ≤ -9
x ≤ -9/5

2. b. It represents, how many carnations needed to be carnations: 11

c . No because the solution is not a sold to break even. Total number of carnations.

1. To find the x-values at which the equations y = x and y = -x + 6 intersect, you need to equate the two equations and solve for x. Set x (from the first equation) equal to -x + 6 (from the second equation).

x = -x + 6

Now, solve for x:

2x = 6

Divide both sides by 2:

x = 3

Therefore, the x-value at which the two equations intersect is x = 3.

2. a. Let's define two variables:

Let x represent the number of carnations sold.
Let y represent the total cost of buying the carnations.

The total cost consists of the cost of the carnations and the delivery charge, so we can express it as:

y = 0.50x + 16

b. To graph this system, plot the cost (y) on the y-axis and the number of carnations (x) on the x-axis. The graph will be a straight line diagonal upwards.

c. The solution to this system represents the break-even point, where the total revenue from selling carnations matches the total cost of buying them. If the graph intersects with the positive side of the y-axis (above zero), it means the school band makes a profit. If it intersects with the negative side of the y-axis (below zero), it means they incur a loss.

If the solution on the graph does not make sense in this situation, it means the band is either selling fewer than zero carnations (which is impossible) or they are making a negative amount of money on each carnation sold (also impossible). So, a reasonable solution might be to adjust the pricing or find a way to cut costs.

3. To solve the equation -x/5 = 12, you want to isolate the variable x. Multiply both sides of the equation by 5:

-5(x/5) = 12 * 5

Simplify:

-x = 60

Now, to solve for x, multiply both sides of the equation by -1 (to cancel out the negative sign in front of x):

(-1)(-x) = (-1)(60)

Simplify:

x = -60

So, the solution to the equation -x/5 = 12 is x = -60.

4. To solve the equation 2/5 = y/12, you need to isolate the variable y. Cross-multiply:

2 * 12 = 5 * y

Simplify:

24 = 5y

Now, solve for y by dividing both sides of the equation by 5:

y = 24/5

Simplify:

y = 4.8

Therefore, the solution to the equation 2/5 = y/12 is y = 4.8.

5. To solve the equation 6(x + 2) = -2(x + 10), you first need to simplify both sides:

6x + 12 = -2x - 20

Combine like terms by adding 2x to both sides:

6x + 2x + 12 = -20

Combine like terms by subtracting 12 from both sides:

8x = -32

Now, divide both sides of the equation by 8:

x = -32/8

Simplify:

x = -4

Therefore, the solution to the equation 6(x + 2) = -2(x + 10) is x = -4.

6. To solve the inequality 4(2x + 1) > 28, you first need to simplify both sides:

8x + 4 > 28

Subtract 4 from both sides of the inequality:

8x > 24

Now, divide both sides of the inequality by 8:

x > 3

Therefore, the solution to the inequality 4(2x + 1) > 28 is x > 3. This means that any value of x greater than 3 will satisfy the inequality.

7. To solve the inequality 1/8x + 3/5 ≤ 3/8, you first need to find a common denominator for all fractions involved. In this case, the least common denominator (LCD) is 40. Multiply every term by 40 to eliminate the fractions:

40 * (1/8)x + 40 * (3/5) ≤ 40 * (3/8)

Simplify each side:

5x + 24 ≤ 15

Now, subtract 24 from both sides of the inequality:

5x ≤ 15 - 24

Simplify:

5x ≤ -9

Finally, divide both sides of the inequality by 5:

x ≤ -9/5

So, the solution to the inequality 1/8x + 3/5 ≤ 3/8 is x ≤ -9/5.