Solving Systems of Equations
by Graphing
by Graphing
Solving Systems of Equations Word Problems
Solving Multi-Step Equations and Inequalities
Miscellaneous
Inequalities
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
Solve the inequalities. x+4<3
x<-1
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
Solve the inequalities. m+13≥14
m≥1
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
Solve the inequalities. -3y>36
y<-12
400
Graph the system of inequalities. Find at least one solution.
y < 3
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
Solve the inequalities. d/-11 ≤6
d≥-66
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
Solve the inequalities.
3+b/3<7
b<12