Solve by ELIMINATION
Solve by GRAPHING
Word Problems
Solve by SUBSTITUTION
100
What variable will be eliminated?
2x-9y=2
x+9y=5
The y variable will be eliminated
100
Find the point of intersection.
(5,2)
100
Brooke volunteered at a local community center to raise money for new sports equipment. Brooke worked the food booth where chicken dinners, x, sold for $13 and hamburgers, y, sold for $3. On Saturday night, Brookes booth earned $172 and sold 24 food items. Write a system of equations to represent the situation.
13x+3y=172
x+y=24
100
Solve the systems of equations using substitution.
x = 5
x + y = 12
(5, 7)
200
When solving by elimination, what do you look for to know which variable will disappear?
Same Coefficient, Different Signs.
200
Find the point of intersection.
None, parallel lines
200
Wyatt volunteered at a local community center to raise money for a new playground. Wyatt worked the food booth where spaghetti dinners, x, were sold for $10 and hamburgers, y, were sold for $2. On Saturday night, Wyatts booth earned $272 and sold 56 items of food. Write a system of equations to represent the situation.
10x+2y=272
x+y=56
200
Solve the systems of equations using substitution.
y = 2x
x + y = 9
(3, 6)
300
What must you do to eliminate the x?
2x-3y=9
2x+7y=1
Multiply either equation by a negative 1
300
(3,-2)
300
Felicity has 30 pottery pieces for sale in her store. Each vase, v, sells for $21 and each bowl, b, sells for $12.50. If Felicity sells all of her inventory, she will make $477.
How many vases and bowls does Felicity's store have for sale?
12 vases
18 bowls
300
Solve the systems of equations using substitution.
y=6x-19
y=-2x+5
(3,-1)
400
What is the solution to the system of equations below.
21x+6y=72
-8x-2y=-30
(6,-9)
400
(4,-4)
400
Martina has 50 cupcakes for sale at her bakery. Each red velvet cupcake, v, sells for $2.75 and each carrot cupcake, c, sells for $3. If Martina sells all of the cupcakes, she will make $142.25. This situation can be represented by the system of equations shown below.
2.75v+3c=142.25
v+c=50
Red Velvet Cupcakes: ________
Carrot Cupcakes:_________
31 red velvet
19 carrot
400
Solve the systems of equations using substitution.
y = 2x
y - 3x = 8
(-8, -16)
500
Solve using elimination method
−4x + 4y = 4
−6x + 3y = −12
(5,6)
500
(2,2)
500
DeShawn and Beth are selling flower bulbs for a school fundraiser. Customers can buy packages of tulip bulbs and packages of crocus bulbs. DeShawn sold 8 packages of tulip bulbs and 7 packages of crocus bulbs for a total of $168. Beth sold 10 packages of tulip bulbs and 14 packages of crocus bulbs for a total of $294. Find the cost each of one package of tulip bulbs and one package of crocus bulbs.
Tulip bulbs $7
Crocus bulbs: $16
500
Solve the systems of equations using substitution.
2x-3y=-24
x+6y=18
(-6,4)