Solving Eqs.
Solve for n.
75 = 3(-6n - 5)
n = -5
Solve and graph the inequality.
0 > 3x - 3 - 6
x < 3
Graph to solve.
y = -5/3x +3
y = 1/3x -3
Solution: (3,2)
The difference of two numbers is 3. Their sum is 13. Find the numbers.
5 and 8
Solve the systems of equations using substitution:
y = -2x - 9
3x -6y = 9
(-3, -3)
Solve for r.
-3(1+6r) = 14 - r
r = -1
When graphing inequalities, which symbols have an open and closed circle? What does this mean on their graph?
open: <, >, dashed line
closed: \<, >/, solid line
Solve by graphing
y = -1
y = -5/2x +4
Solution: (2,-1)
The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.
senior citizen ticket: $8, child ticket: $14
Solve the systems of equations using substitution:
2x - y = 6
x = y + 5
(1, -4)
Solve for k.
-4k +2(5k-6)= -3k -39
k = -3
How is graphing systems of inequalities different than graphing systems of equations?
Lines may be dotted, and you must shade the solution region.
y = -2x + 2
y = -2x - 2
NO SOLUTION
Ms. Panek tells you that the next test is worth 100 points and contains 38 problems. Multiple-choice questions are worth 3 points and word problems are worth 4 points. How many of each type of questions are in there?
8 word problems
30 multiple choice
Solve this by elimination:
2x - y = 4
x + 3y = 3
(3,2)
Explain 2 ways you could solve 20 = 5(-3 + x), then solve for x.
2. Distribute the 5 first
x = 7
y ≤ x − 2
y > −3x + 5
Is (5,2) a solution to the system?
Yes.
Solve by graphing:
y > -x - 2
y < -5x + 2
Intersection: (1,-3)
Dotted lines
Shade toward orgin
Adult tickets for the school musical sold for $3.50 and student tickets sold for $2.50. On a given night, 321 tickets were sold for $937.50. How many of each kind of ticket were sold?
adults-135
Children- 186
Use Elimination method to solve:
−8x − 10y = 24
6x + 5y = 2
(7,-8)
Solve for k.
12(2k + 11) = 12(2k +12)
No solution.
A university will spend at most $4,500 to buy monitors and keyboards for a computer lab. Each monitor will cost $250 and each keyboard will cost $50.
Write an inequality that will represent all the combinations of x, the number of monitors and y, the number of keyboards, the university can buy.
250x + 50y /< 4,500
Solve by graphing:
3x+2y >/ -2
x + 2y \< 2
Intersection: (-2,2)
Solid lines
Shade toward orgin
The sum of two numbers is 30 and their difference is 12. Find the two numbers.
(21, 9)
Solve the systems of equations using substitution:
y=2x-10
y=4x+8
(-9,-28)