Substitution
Solve the systems of equations using the substitution method.
y = 6x - 8
x = -3
(-3,-26)
Solve the systems of equations using the elimination method.
4x + 8y = 20
-4x + 2y = -30
(7, -1)
There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many of each animal are there?
7 pigs & 6 chickens
Where would you find a solution to a system of linear inequalities?
In the overlapping shaded region
Solve the systems of equations using the substitution method.
4x + 5y = 40
y = 4
(5,4)
Solve the systems of equations using the elimination method.
8x + y = -16
-3x + y = -5
(-1, -8)
A farmhouse shelters 10 animals. Some are pigs and some are ducks. Altogether there are 36 legs. how many of each animal are there?
8 pigs & 2 ducks
What would you call a point that is outside the shaded region?
Not a solution
Solve the systems of equations using the substitution method.
y = -3x + 1
y = 2x - 4
(1,-2)
Solve the systems of equations using the elimination method.
-4x + 9y = 9
x - 3y = -6
(9,5)
A class of 195 students went on a field trip. They took 7 vehicles, some cars and some buses. Find the number of cars and buses they took if each car holds 5 students and each bus holds 45 students.
3 cars & 4 buses
Graph the system of linear inequalities.
y > 4x - 3
y >/ -2x + 3
One dashed line, one solid line making an x & intersecting at about (1,1). Overlapping shading at the top of the x.
Solve the systems of equations using the substitution method.
y = 8x - 2
y = 3x + 8
(2,14)
Solve the system of equations using the elimination method.
5x + 4y = -14
3x + 6y = 6
(-6,4)
Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. She bought a total of 7 shirts. How many of each kind did she buy?
5 plain shirts & 2 fancy shirts
Graph the system of linear inequalities.
y >/ -5x + 3
y > -2
One solid line, one dashed (horizontal) line intersecting at about (1, -2). Overlapping shading in upper right corner.
Solve the systems of equations using the substitution method.
6x - 3y = 9
y = -x - 9
(-2,-7)
Solve the systems of equations using the elimination method.
2x + 8y = 6
-5x - 20y = -15
Infinitely Many Solutions
(IMS)
Molly's Custom Kitchen Supplies sells handmade forks and spoons. It costs the store $1.70 to buy the supplies to make a fork and $1.30 to buy the supplies to make a spoon. The store sells forks for $5.60 and spoons for $5.40. Last April Molly's Custom Kitchen Supplies spent $37.90 on materials for forks and spoons. They sold the finished products for a total of $147.20. How many forks and how many spoons did they make last April?
7 forks & 20 spoons
Graph the system of linear inequalities.
y < -x - 3
y > -x +4
Two dashed parallel lines. No overlapping shading, meaning the answer is NO SOLUTION.