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Solving Systems of Equations
by Graphing
Solving Systems of Equations Word Problems
Solving Multi-Step Equations and Inequalities
Miscellaneous
Interval Notation
100
Solve the system of linear equations by graphing. y = 2x + 5 y = 1/2x - 1
Solution: (-4, -3)
100

Write a system of equations for the situation. Solve by elimination. A landscaper buys 4 peonies and 9 geraniums for $190. Another landscaper buys 5 peonies and 6 geraniums for $185. Write and solve a system of linear equations to find the cost of each peony.

4x + 9y = 190 Solution: x = 25; $25 per peony 5x + 6y = 185

100

(-1/3)(9x +42) -5x = -70

Solve for x

x=7

100

On your whiteboard draw me a graph that has an undefined slope and give me the equation of that graph.

answers can vary

100
When do you use an open circle on the number line?

When do you use the closed circle?

Brackets and Greater Than or Equal To and Less than or equal to

Parenthesis and less than or greater than

200
Solve the system of equations by graphing. y = -x - 4 y = 3/5x + 4
Solution: (-5, 1)
200
Write a system of equations for the following situation. Then solve by graphing. A kicker on a football team scores 1 point for making an extra point and 3 points for making a field goal. The kicker makes a total of 8 extra points and field goals in a game and scores 12 points. Write and solve a system of linear equations to find the number x of extra points and the number of field goals. Explain what the solution means.
System: x + y = 8 Solution: (6, 2) x + 3y = 12 The kicker made 6 extra points and 2 2 field goals.
200

7(3r-1) - (r+5) = -52

Solve for r

r=-2


200
Find the slope of the line through the given points. (1, -2), (7, -2)
0
200

What is the interval notation of x>-3?

(-infinity, -3)

300
Solve the system of equations by graphing. y = 1.5x - 2 y = -x + 6
Solution: (3, 3)
300
Write a system of linear inequalities for this situation. Graph the inequalities. You can spend at most $21 on fruit. Blueberries cost $4 per pound and strawberries cost $3 per pound. You need at least 3 pounds to make muffins. Is it possible to buy 4 pound of blueberries and 1 pound of strawberries in this situation?
x = pounds of blueberries x + y > 3 (or equal to) y = pounds of strawberries 4x + 3y < 21 ( or equal to) Yes this is more than 3 pounds and costs $19, which is less than $21.
300

-4(2x+1) =-3x -5x -2

No Solution

300

Rewrite in slope-intercept form: -2x + 3y = -6

y = 2/3x - 2

300

[-4,∞) write in inequality form

x≥4 

400
Graph the system of inequalities. Find at least one solution. y < 3 (less than or equal to) y > x + 2
Ex: One solution is (-3, 1)
400
You can spend at most $60 on lace. Cotton lace is $2 per yard and linen lace is $3 per yard. Write an inequality for the amounts of lace you can buy. Can you buy 12 yards of cotton lace and 15 yards of linen lace? Explain
2x + 3y < 60 (or equal to) No you cannot buy 12 yards of cotton lace and 15 yards of linen lace because (12, 15) is not a solution of the inequality.
400
Solve the equation. 5(4w - 20) = 4(5w - 25)
infinitely many solutions
400

Write a system of linear inequalities represented by the graph shown.

y < 1/2x + 4 (or equal to) y > 3/2x + 1

400

(-∞,2) U [4,∞)

x<2 or x≥4 

500
Graph the system of linear inequalities. Describe the solution. 2x + y < -1 2x + y > 3
No solution
500
Write a system of equations for the situation. Solve the system by substitution. There are a total of 64 students in a drama club and a yearbook club. The drama club has 10 more students than the yearbook club. How many students are in the drama club? the yearbook club?
x + y = 64 y + 10 + y = 64 x = 27 + 10 2y + 10 = 64 x = 37 x = y + 10 2y = 54 y = 27 drama: 37 students yearbook: 27 students
500
Tell whether the ordered pair is a solution of the system of linear inequalities. y < 5 (-1, 5) y > x - 4
5 is not less than 5 No
500

ax+by=c

solve for y

(c-ax)/b

500

(-∞,∞)  What does this mean?

All Real Numbers