Solving Systems
Special Systems
Parallel and Perpendicular Lines
Inequalities
Systems of Inequalities
100
Is the point (-5,2) a solution to the system below?
y=3x+10
y=-x-3
No, the point does not satisfy the equation
y=3x+10
100
Determine whether the system has one solution, no solution, or infinitely many solutions. Explain.
The system has no solution because the lines are parallel and will never intersect.
100
The slope of a line is -8.
What is the slope of the parallel line? What is the slope of the perpendicular line?
Parallel slope: -8
Perpendicular slope: 1/8
100
Is the ordered pair (-2,-2) a solution to the inequality shown on the graph? Explain.
No, the ordered pair is on a dashed boundary line, so it is not included in the solution set.
100
Is the ordered pair (-3,1) a solution of the system of linear inequalities? Explain.
No, the point is on the dashed line, which means it is not included in the solution set.
200
Use the graph to solve the system:
The solution is (3,1).
200
Determine whether the system has one solution, no solution, or infinitely many solutions. Explain.
The system has infinitely many solutions because the lines are the same.
200
Which lines are parallel? Explain.
Lines b and c are parallel (red and green lines) because they have the same slopes (-2)
200
Is the ordered pair (-8,2) a solution of the inequality
-x-6y>12?
No, the point does not satisfy the inequality.
200
Is the ordered pair (4,-3) a solution of the system of linear inequalities?
y<=-x+1
y<=5x-2
Yes, the point satisfies both inequalities.
300
Solve the system.
y=x+4
y=-x+8
The solution is (2,6).
300
Determine whether the system of linear equations has one solution, no solution, or infinitely many solutions. Explain.
y=-2x-4
y=2x-4
The system has one solution because the slopes are different. The lines will intersect.
300
Which lines are perpendicular? Explain.
Line a:
y=6x-2
Line b:
6y=-x
Line c:
y+6x=1
Lines a and b are perpendicular because they have opposite reciprocal slopes (6 and -1/6)
300
Write an inequality that represents the graph.
y<=2
300
What is one solution to the system of linear inequalities?
y<=3x+4
y>1/2x+2
Any point in the double-shaded region:
400
Solve the system.
4x+5y=3
-3x+2y=38
The solution is (-8,7).
400
Solve the system.
15x-5y=-20
-3x+y=4
The system has infinitely many solutions.
400
Write an equation of the line that passes through (-4,-1) and is parallel to
y=4/3x+6
y=4/3x+13/3
400
Write an inequality that represents the graph.
y>1/2x+2
400
Write a system of linear inequalities represented by the graph:
y>=2/3x-2
y>=-3x+2
500
You sell bracelets for $2 each and necklaces for $3 each at a local flea market. You collect $95, selling a total of 37 jewelry items. How many of each type of jewelry did you sell?
You sold 16 bracelets and 21 necklaces.
500
Solve the system.
y=-6x-2
12x+2y=-6
The system has no solution.
500
Write an equation of the line that passes through (8,1) and is perpendicular to the line
2y+4x=12
y=1/2x-3
500
You have at most $20 to spend at an arcade. Arcade games cost $0.75 each, and snacks cost $2.25 each. Write an inequality that represents the numbers of games you can play and snacks you can buy.
x= # of games
y= # of snacks
0.75x+2.25y<=20
500
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 of fruit to make muffins. Write a system of linear inequalities that represents the situation.
x= pounds of blueberries
y=pounds of strawberries
4x+3y<=21
x+y>=3