# Simultaneous Equations

**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. $12.75$ |

## Number of Civil, Electrical, and Mechanical Engineers and Their Average Ages

**Problem**

In an organization there are CE’s, EE’s and ME’s. The sum of their ages is 2160; the average age is 36; the average age of CE’s and EE’s is 39; the average age of EE’s and ME’s is 32 and 8/11; the average age of the CE’s and ME’s is 36 and 2/3. If each CE had been 1 year older, each EE 6 years and each ME 7 years older, their average age would have been greater by 5 years. Find the number of CE, EE, and ME in the group and their average ages.

## Example 07 - Simultaneous Non-Linear Equations of Two Unknowns

**Problem**

Solve for $x$ and $y$ from the given system of equations.

$\dfrac{3}{x^2} - \dfrac{4}{y^2} = 2$ ← Equation (1)

$\dfrac{5}{x^2} - \dfrac{3}{y^2} = \dfrac{17}{4}$ ← Equation (2)

## Example 06 - Simultaneous Non-Linear Equations of Two Unknowns

**Problem**

Solve for $x$ and $y$ from the given system of equations.

$x^2y + y = 17$ ← Equation (1)

$x^4y^2 + y^2 = 257$ ← Equation (2)

## Smallest number for given remainders

## Example 04 - Simultaneous Non-Linear Equations of Three Unknowns

**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)

## Example 03 - Simultaneous Non-Linear Equations of Three Unknowns

**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)

## Example 02 - Simultaneous Non-Linear Equations of Three Unknowns

**Problem**

Find the value of *x*, *y*, and *z* from the following equations.

$xy = -3$ → Equation (1)

$yz = 12$ → Equation (2)

$xz = -4$ → Equation (3)