Problem
Solve for x from the following equations:
| $xy = 12$ | $yz = 20$ | $zx = 15$ |
| A. 2 | C. 4 |
| B. 3 | D. 5 |
Problem
Given the following equations:
$$ab = 1/8 \qquad ac = 3 \qquad bc = 6$$
Find the value of $a + b + c$.
| A. $12$ | C. $\dfrac{4}{51}$ |
| B. $\dfrac{7}{16}$ | D. $12.75$ |
Problem
Solve for x, y, and z from the following simultaneous equations.
$x^2 - yz = 3$ ← Equation (1)
$y^2 - xz = 4$ ← Equation (2)
$z^2 - xy = 5$ ← Equation (3)
Problem
A nutritionist in a hospital is arranging special diets that consist of a combination of three basic foods. It is important that the patients on this diet consume exactly 310 units of calcium, 190 units of iron, and 250 units of vitamin A each day. The amounts of these nutrients in one ounce food are given in the following table.
| Units Per Ounce | |||
| Calcium | Iron | Vitamin A | |
| Food A | 30 | 10 | 10 |
| Food B | 10 | 10 | 30 |
| Food C | 20 | 20 | 20 |
How many ounces each food must be used to satisfy the nutrient requirements exactly?
Problem
Solve for x, y, and z from the following system of equations.
$x(y + z) = 12$ → Equation (1)
$y(x + z) = 6$ → Equation (2)
$z(x + y) = 10$ → Equation (3)
Problem
Find the value of x, y, and z from the given system of equations.
$x(x + y + z) = -36$ → Equation (1)
$y(x + y + z) = 27$ → Equation (2)
$z(x + y + z) = 90$ → Equation (3)
The number of equations should be at least the number of unknowns in order to solve the variables. System of linear equations can be solved by several methods, the most common are the following,
1. Method of substitution
2. Elimination method
3. Cramer's rule
Many of the scientific calculators allowed in board examinations and class room exams are capable of solving system of linear equations of up to three unknowns.
Problem
Solve for x, y, and z from the following simultaneous equations.
$z^x \, z^y = 100\,000$ ← equation (1)
$(z^x)^y = 100\,000$ ← equation (2)
$\dfrac{z^x}{z^y} = 10$ ← equation (3)
