Graphing Systems of Equations
Systems that have at least one solution are called...
Consistent
Solve the system of equations using substitution: 2x+y=6 and 6x+2y=4.
(-4, 14)
Why do we use linear programming?
To identify a minimum or maximum value of some quantity. It is often used to make improvements to businesses and companies.
The third plane added in a three-dimensional plane is called the...
z-axis
What is this symbol? >
greater than
Systems that have no solution are called...
Inconsistent
Solve the system of equations using elimination: -8x-10y=28 and 4x+10y=-24.
(-1, -2)
Limits on the variables in the objective function that are written as linear inequalities are called...
Constraints
What is the notation of (x, y, z) called?
Ordered Triples
When you graph the absolute value of an equation and the equation has the symbol <, will you shade the part above the v or the part below the v?
below
Graph the system of equations to find the solution: y=-x-2 and y=4x+3.
(-1, -1)
Solve the system of equations using substitution: 2x+4y=7 and x+2y=3.
No Solution
What points do we choose as the possible maximums or minimums that we plug into the objective function?
The vertices of the feasible region.
The lines connecting the intercepts on the graph of a 3-D equation are called...
Traces
Solve the following system of inequalities by graphing: y<3x-2 and y>3x+3.
No Solution because the shaded regions will never overlap (the lines are parallel)
Graph the systems of equations to find the solution: -2x+y=4 and -2y=-4x+12.
No Solution because the lines are parallel.
Solve the system of equations using elimination: -4x-8y=8 and 8x+16y=-16.
Infinite Number of Solutions
Given the objective function P=300x+250y, which of the following points are the maximum? (0, 0), (2, 1), (1, 3), or (0, 4).
(1, 3)
What are the x, y, and z intercepts of the equation 3x+2y-4z=12?
x=4, y=6, and z=-3
Solve the following system of equations by graphing: x+y>-3 and x+y<3.
Graph the lines. The lines should both be dotted. The lines should be parallel and you should shade the region between the two lines.
Without graphing, classify this system of equations as either inconsistent, consistent and dependent, or consistent and independent. 3x-18y=9 and -6y+x=3
Consistent and dependent
Determine if the point (7, 3) is a solution to the system of equations: 5x+5y=20 and x-2y=13.
No, it is in fact, not.
Given the objective function P=55x+80y which of the following points are the minimum? (1, 4), (4, 1), (3, 2) or (2, 3)
(4, 1)
Instead of graphing in a coordinate plane, we graph in a coordinate ______________ for 3-D graphs.
Space
Determine if (10, 10) is a solution to the system: y<2x-1 and y>=10-x.
Yes, it in fact, is.