Equations and inequalities: linear simultaneous equations
Thus far, all equations that have been encountered have one unknown variable that must be solved for. When two unknown variables need to be solved for, two equations are required and these equations are known as simultaneous equations. The solutions to the system of simultaneous equations are the values of the unknown variables which satisfy the system of equations simultaneously, that means at the same time. In general, if there are
$n$ unknown variables, then
$n$ equations are required to obtain a solution for each of the
$n$ variables.
An example of a system of simultaneous equations is:
In order to find a numerical value for an unknown variable, one must have at least as many independent equations as variables. We solve simultaneous equations graphically and algebraically.
Graphical solution
Simultaneous equations can be solved graphically. If the graph corresponding to each equation is drawn, then the solution to the system of simultaneous equations is the co-ordinate of the point at which both graphs intersect.
A common algebraic technique is the substitution method: try to solve one of the equations for one of the variables and substitute the result into the other equations, thereby reducing the number of equations and the number of variables by 1. Continue until you reach a single equation with a single variable, which (hopefully) can be solved; back substitution then allows checking the values for the other variables.
In the example
[link] , we first solve the first equation for
$x$ :
$$x=\frac{1}{2}-y$$
and substitute this result into the second equation:
A shop sells bicycles and tricycles. In total there are 7 cycles (cycles includes both bicycles and tricycles) and 19 wheels. Determine how many of each there are, if a bicycle has two wheels and a tricycle has three wheels.
The number of bicycles and the number of tricycles are required.
If
$b$ is the number of bicycles and
$t$ is the number of tricycles, then:
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest.
Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.?
How this robot is carried to required site of body cell.?
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Rafiq
The nanotechnology is as new science, to scale nanometric
brayan
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Damian
Is there any normative that regulates the use of silver nanoparticles?