Classify each system
Solve each system algebraically
Write a system of equations
Solve by Graphing
Reasoning
100
y = 3x - 4; 2y = 6x - 8
Consistent Dependent
100
x - 2y = 3; 3x + y = -5
(-1, -2)
100
For $7.52 you purchased 8 pens and highlighters from a local bookstore. Each highlighter cost $1.09 and each pen cost $0.69. Write a system of equations to model the problem.
let h = # of highlighters bought let p = # of pens bought 1.09h + 0.69p = 7.52 h + p = 8
100
y = 3x - 1; y = 6x + 2
(-1, -4)
100
Is it possible for an inconsistent linear system to contain two lines with the same y-intercept? Explain.
No, they would be the same line and the system would be dependent and consistent.
200
6x - 2y = 2; 2 + 6x = y
Consistent Independent
200
11 - 5y = 2x; 5y + 3 = -9x
(-2, 3)
200
A student took 60 minutes to answer a combo of 20 multiple choice and extended-response questions. She took 2 minutes to answer each multiple choice question and 6 minutes to answer each extended-response question. Write a system of equations to model the problem.
let m = # of multiple choice questions let r = # of extended-response questions m + r = 20 2m + 6r = 60
200
y + 5 = 2x; 3y = -6x - 3
(1, -3)
200
In a system of linear equations, the slope of one line is the negative reciprocal of the slope of the other line. Is this system independent, dependent, or inconsistent?
Independent; if the slope of one equation is the opposite reciprocal of the slope of the other equation, the lines are perpendicular and will intersect at a unique point.
300
5 - y = 2x; 6x - 15 = -3y
Consistent Dependent
300
2x + 3y = 4; 4x + 6y = 9
inconsistent; no solution
300
An entrance exam has two sections, a verbal section and a math section. You can score a maximum of 1600 points. For admission, the school of your choice requires a math score of at least 600. Write a system of inequalities to model scores that meet the school's requirement.
let v = verbal scores let m = math scores v + m ≤ 1600 m ≥ 600
300
y ≤ | x + 2 | - 3; y ≥ 1 + ¼ x
See document camera
300
Explain how the graphical solution of the system of inequalities is different from the graphical solution of a system of equations.
Graphical solution of system of inequalities consists of an overlap or intersection of boundary lines (shading). Graphical solution of a system of equations includes only the intersection of the lines.
400
6y + 2x = 8; 12y + 4x = 4
Inconsistent
400
3x + y - 2z = 22; x + 5y + z = 4; x = -3z
(6, 0, -2)
400
For a community breakfast there should be at least three times as much regular coffee as decaffeinated coffee. A total of ten gallons is sufficient for the breakfast. Write a system of inequalities to model the problem.
let r = amount of regular coffee let d = amount of decaffeinated coffee r + d ≤ 10 r ≥ 3d
400
y < | 2x -4 |; x + 5y ≥ -1
See document camera
400
Explain how you determine where to shade when solving a system of inequalities.
If the isolated variable, y, is greater than the remaining expression, the half-plane above the boundary line is shaded. If it is less than the remaining expression, the half-plane below the boundary line is shaded.
500
1.5 + 3x = 0.5; 6 - 2y = -12x
Consistent Dependent
500
x + y - 2z = 8; 5x - 3y + z = -6; -2x - y + 4z = -13
(1, 3, -2)
500
In a factory there are three machines: A, B, C. When all three machines are working, they produce 287 bolts per hour. When only machines A and C are working, they produce 197 bolts per hour. When only machines A and B are working, they produce 202 bolts per hour. Write a system of equations to model the problem.
let A = machine A bolts per hour let B = machine B bolts per hour let C = machine C bolts per hour A + B + C = 287 A + C = 197 A + B = 202
500
y > -2; y ≤ - | x – 3 |
See document camera
500
How do you decide whether substitution is the best method to solve a system in three variables?
Substitution is the best method to use when one of the equations can be solved easily for one variable.
M
e
n
u