Simultaneous Equations

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.   $12.75$

 

Example 05 - Simultaneous Non-Linear Equations of Three Unknowns

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)
 

Solution

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

Problem
Find the smallest number which when divided by 2 the remainder is 1, when divided by 3 the remainder is 2, when divided by 4 the remainder is 3, when divided by 5 the remainder is 4, and when divided by 6 the remainder is 5.
 

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)
 

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