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Systems of linear equations are so important because they give you an easy way to do mass and complex mathematical calculations. For example:
x/2 + y/4 = 255,
3x - y/2 = 100.
The first step is to solve the first equation for y:
2x + y = 1020,
y = 1020 - 2x.
Substitute that value of y into the second equation and solve for x:
3x - (1020 - 2x)/2 = 100,
3x - 510 + x = 100,
4x = 610,
x = 152.5.
Finally, substitute that value of x into the first equation to get the solution for y:
152.5/2 + y/4 = 255,
y/4 = 178.75,
y = 715.
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What are linear equtions and simultanions equations?
Linear Equations are equations with variable with power 1 for eg: 5x + 7 = 0 Simultaneous Equations are two equations with more than one variable so that solving them simultaneously
How mathematics is related to electricity?
Electrical engineering uses many branches of mathematics including complex numbers, matrices and linear equations. To study machines needs dynamics and thermodynamics. Radio systems use the theory of electromagnetics that uses vector algebra and optionally tensor algebra. Many branches of electrical engineering use the theory of differential equations and functions of a complex variable. So if you are good at mathematics electricity gives plenty of scope.
How do you solve systems of linear equations by elimination with decimal coefficient?
I will give a simple example just to illustrate the idea, but all you have to do is multiply any of the equations by a constant to make them inversely additive values and add the equations. .2x-.5y = 10 .5x+.3y = 15 .2 = 1/5 and .5 = 1/2 so if I multiply the first equation by -5 and the second by 2, we get the system: -x+2.5y = -50 x+.6y = 30 (-x+2.5y = -50) + (x+.6y = 30) = (3.1y = -20) Solving for the variables, we get y = -6.452 and x = 33.871
What does solving a system of equations actually mean?
That means to find values for all the variables involved, so that they satisfy ALL the equations in a system (= set) of equations.That means to find values for all the variables involved, so that they satisfy ALL the equations in a system (= set) of equations.That means to find values for all the variables involved, so that they satisfy ALL the equations in a system (= set) of equations.That means to find values for all the variables involved, so that they satisfy ALL the equations in a system (= set) of equations.
How many linear ft is in 2000 ft?
Feet is a linear measurement, so feet and linear feet are the same. So, you could say 2000 linear feet instead of just 2000 feet.
How are linear equations and functions alike?
They are not. A vertical line is not a function so all linear equations are not functions. And all functions are not linear equations.
What are linear equtions and simultanions equations?
Linear Equations are equations with variable with power 1 for eg: 5x + 7 = 0 Simultaneous Equations are two equations with more than one variable so that solving them simultaneously
Is the equation 3x-4 equals 12 linear or non linear?
It is a linear equation. The highest power of x in the equation is 1 (3x1-4=12) so its "degree" is 1, and equations of "degree 1" are called linear equations.
Whats the difference between a linear equation and a system of linear equations?
Quite simply, the latter is a group of the former.A system of linear equations is several linear equations taken together, each using the same group of unknowns. Usually, such a system provides one linear equation for each unknown (x, y, z, et al) that must be found (more complex systems can exist, though). You can use and manipulate these linear equations as you would a single linear equation to help solve for the unknowns. One way is to reduce all but one of the unknowns so that each can be expressed in terms of the remaining unknown and then solve for the remaining unknown which would in turn give you the others.
Using linear equations in real life?
I image you intends algebraic linear equations. A great number of problems in real life are mathematically model with algebraic linear equations like - Design of electronic filters for any application (smart-phones, stereo systems, radio systems, ....) - Optimization of the any problem that can be modeled with the so called simplex algorithm (commercial programs uses this set of linear equations to optimize management of a civil airplane company, of the production in a car factory, of the management of a warehouse and many other problems) - The determination of currents and voltages in an electrical circuit composed of resistances, inductive elements, capacitors and ideal amplifiers can be done by a system of algebraic linear equations; This is only a very limited set of examples. However in mathematics any equation, not only algebraic, but also integral, differential and so on, is called linear if the sum of two solutions is again a solution and the product of a solution by a number is again a solution. You can easily verify that it is true also for homogeneous algebraic equations (that is linear angebraic equations without the known term). For example if we have the two unknown x and y the equation 2x+y=0 is linear. As a matter of fact, since x=1, y=-2 is a solution and x=-2, y=4 is another solution, also the sum of the two solutions, that is x=-1, y=2 is another solution. If we adopt this extended definition, the quantum mechanical basic equations are linear, thus we can say that, up to the moment in which we do not consider cosmic bodies for whom gravity is important, the whole world is linear !!
Who found about linear equations?
Linear equations, maybe not in a form you would recognize, have been around since the ancient Greeks, and maybe before them in China. Diophantus around 250AD wrote about equations. But there was work in that area before him. So there is no single 'who' but like many other things it is a building of knowledge over a long period of time that has evolved into what we now call linear equations.
Example equations of linear equations?
y=3x+2 y-4x=9 These are examples of linear equations which is a first degree algebraic expression with one, two or more variables equated to a constant. So x=2 is a linear equation as is y=1 but x2 =1 is not since the variable, x , has degree 2.
What are the three ways of solving system of linear eqution?
Systems: 1. Solve for a letter and substitute into the other equation. It is called substitution. 2. Linear combination. Set the equations so the letters match up. Multiply one of the equations so one of the letters will go to zero when yoy add them together and solve for the other letter. 3. Determinants. Setting up square matrix and substituting into the matrix to find the different variables.
Does the range of linear equations have all real numbers?
No. For example, linear algebra, for example, is about linear equations where the domain and range are matrices, not simple numbers. These matrices may themselves contain numbers that are real or complex so that not only is the range not the real numbers, but it is not based on real numbers either.
Why are systems of linear inequality so important?
A system of linear inequalities give you a set of answers that could work. In day to day lives we actually use linear inequalities all the time. We are given questions and problems where we search for a number of possible solutions.
How does the bisection method work when solving nonlinear equations?
it works exactly the same as it does with linear equations, you don't need to do any differentiation or anything fancy with this method, just have to plug in values of x, so it shouldn't make a difference if the equation is linear or nonlinear.
How do you solve linear equations using linear combinations?
Solving linear equations using linear combinations basically means adding several equations together so that you can cancel out one variable at a time. For example, take the following two equations: x+y=5 and x-y=1 If you add them together you get 2x=6 or x=3 Now, put that value of x into the first original equation, 3+y=5 or y=2 Therefore your solution is (3, 2) But problems are not always so simple. For example, take the following two equations: 3x+2y=13 and 4x-7y=-2 to make the "y" in these equations cancel out, you must multiply the whole equation by a certain number.
