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Graphing Method
Substitution Method
Elimination Method
Inequalities
Real Life
100
y = x - 2, y = -x + 4, Please state the coordinates of intersection
Intersection occurs at (3, 1)
100
y = 3x - 10, y = 5x + 14, Solve using the substitution method
(-12, -46)
100
3x + 2y = 4, 3x - 2y = -4, Solve using the elimination method
(0, 2)
100
Please solve the inequality and graph the solution on a number line. 2x +3 >= 5
x >= 1, closed circle; shade right
100
You need some repair work done on your truck. Towne Truck charges $80 just to examine the truck and $30 per hour for labor costs. World Transport Company charges $50 for the initial exam and $40 per hour for the labor. Write a cost equation for each company.
y = 80 +30x y = 50 + 40x
200
y = -x + 7, y = x + 1, Please state the coordinates of intersection
Point of intersection occurs at (3, 4)
200
y = 2x + 3, y = -x + 6, Solve using the substitution method
(1, 5)
200
3x + 2y = 7, -3x + 4y = 5, Solve using the elimination method
(1, 2)
200
Please solve the inequality and graph the solution on a number line. -3x + 14 < 32
x > -6, open circle; shade right
200
It cost $40 for labor to use hand trucks to load each boxcar. After purchasing a forklift for $2000, it costs only $15 for labor to load each boxcar using that forklift. Write an equation that models the cost, C(n) of loading n amount of boxcars with a hand truck.
C(n) = 40n
300
y = 2x + 6, y = -3x - 14, Please state the coordinates of intersection
Point of intersection occurs at (-4, -2)
300
2x = 12, x - 5y = -29, Please solve for x and y
x = 6 y = 7
300
x + 2y = 13, -x + y = 5,
(1, 6)
300
Please solve the inequality and graph the solution on a number line. 3x - 1 <= 4x + 5
x >= -6, closed circle; shade right
300
You own a hot dog stand and your profit made by selling hot dogs is determined by the expression 1.5x - 50. The quantity 1.5 is the profit for each hot dog sold. The cost of leassing the hot dog stand is 50 in the expression 1.5x - 50. Set up an inequality that can be used to determine the amount of hot dogs you have to sell to ensure at least a $2000 profit.
1.5x - 50 >= 2000
400
x + y = 5, y - 2x = -4, Please state the coordinates of intersection
Point of intersection occurs at (3, 2)
400
6x - 9 = y, y = -3x, Solve using substitution
(1, -3)
400
x + y = 2, 2x + 7y = 9, Solve using the elimination method
(1, 1)
400
Please solve the inequality and graph the solution on a number line. -5 <= 3x - 8 < 7
1 <= x < 5, left circle is closed, right circle is open, shade in between circles.
400
The following equation is used in meteorology to determine the temperature and humidity index: T = 2/5(w + 80) + 15 For what values of T would range from 70 to 75? Don't solve, just set up the compound inequality
70 < 2/5(w+80) + 15 <= 75
500
2x - y = -2, 2x + 4y = 8, Please state the coordinates of intersection
Point of intersection occurs at (0, 2)
500
y = 3x + 7, 2x - 5y = 4, Solve using the substitution method
(-3, -2)
500
4x - 3y = 8, 5x - 2y = -11, Solve using the elimination method
(-7, -12)
500
Please solve the inequality and graph the solution on a number line. -2 < (x/3) + 1 < 5
-9 < x < 12, both circles are open; shade in between
500
A catering service placed an order for eight centerpicees and five glasses, and the bill was $106. FOr the wedding reception, they were short one centerpiece and six glasses and had to reorder. This order came to $24. Let x represent the cost of one centerpiece, and let y represent the cost of one glass. Write a system of equations that represents both orders.
8x + 5y = 106 x + 6y = 24