2. What is a linear system?
Two equations solved together – usually
finding the solution of an ordered pair
that satisfied both equations.
3. What are the three ways to solve a linear
system?
1) Graphing the two equations
2) Substitution (solving for x or y)
3) Linear combination – add the two
equations into one and solving
4. Is (-2, 1) a solution for this linear
system?
6x – 3y = - 15
2x + y = - 3
Yes – it is a
solution
5. Is (3, -6) a solution for this linear
system?
x + 3y = 15
No – it is not a
4x + y = 6 solution.
8. Substitution
Solve the linear system using
substitution
x + 2y = 4
-x+y=-7
Solution is (6, -1)
9. Applications
You are painting white lines around the
perimeter of a swimming pool. The
perimeter is 400 feet and the length is 70
feet more than the width.
Let w = width and l = length, find the
length and width of the pool.
65 x 135 feet
10. Substitution
Solve the linear system using
substitution
x + 6y = 15
x = 2y
Solution is (3 3/4, 1 7/8)
15. Applications
You have 50 tickets to ride the Ferris
Wheel and the roller coaster. If your ride
12 times, using 3 tickets for each Ferris
Wheel ride and 5 tickets for each roller
coaster ride, how many times did you go
on each ride?
x + y = 12 3x + 5y = 50
F. Wheel = 5 times, R. C. = 7 times