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Magazine Problem 7
The graph of a linear equation in two variables is a line in a two-dimensional coordinate system. The graph of a linear equation in three variables is a _____ in a three-dimensional coordinate system.
Problem 8
When setting up a partial fraction decomposition, if a fraction has a linear denominator, then the numerator should be (constant/linear). That is, should the numerator be set up as \(A\) or \(A x+B ?\)
Problem 8
Write an inequality to represent the given statement. The value of \(y\) is at least 10 , but less than 20 .
Problem 8
Determine if the ordered pair is a solution to the system of equations. (See Example 1\()\) \(-11 x+6 y=-4\) \(7 x+3 y=23\) a. \(\left(1, \frac{7}{6}\right)\) b. (2,3)
Problem 9
Determine if the ordered pair is a solution to the system of equations. (See Example 1\()\) \(y=\frac{3}{2} x-5\) \(6 x-4 y=20\) a. (2,-2) b. (-4,-11)
Problem 9
Find three ordered triples that are solutions to the linear equation in three variables. $$ 2 x+4 y-6 z=12 $$
Problem 9
For a constant real number \(k\), the inequality \(y>k\) represents the half-plane (above/below) the (horizontal/ vertical) line \(y=k\).
Problem 9
The process that maximizes or minimizes a function subject to linear constraints is called _____ programming.
Problem 9
When setting up a partial fraction decomposition, if the denominator of a fraction is a quadratic polynomial irreducible over the integers, then the numerator should be (constant/linear). That is, should the numerator be set up as \(A\) or \(A x+B ?\)
Problem 10
Find three ordered triples that are solutions to the linear equation in three variables. $$ 3 x-5 y+z=15 $$
