Linear Algebra is a branch of mathematics that enables you to solve many linear equations at the same time. For example, if you had 15 lines (linear equations) and wanted to know if there was a point where they all intersected, you would use Linear Algebra to solve that question. Linear Algebra uses matrices to solve these large systems of equations.
When you have a system of equations and you can solve for one in terms of th others and then replace it in the other equations that is substitution. x+y=15 x-y=1 well the second one can be x=1+y x+y=15 then can be (1+y)+y=15 by substitution. 1+2y=15 2y=14 y=7 Then x+7=15 x=8
Which of the following equations could be used to solve for the tenth term of the following sequence?15, 13, 11, 9, ...
Add the two equations: 3x = 15 Divide by 3: x = 5, making y = -3. Job done.
I guess you mean, you want to add two equations together. The idea is to do it in such a way that one of the variables disappears from the combined equation. Here is an example:5x - y = 15 2x + 2y = 11 If you add the equations together, no variable will disappear. But if you first multiply the first equation by 2, and then add the resulting equations together, the variable "y" will disappear; this lets you advance with the solution.
Your question lacks precision in its expression, but basically you divide the both sides by the coefficient of the unknown. Example: solve 3x = 15. Divide both sides by 3 to get x = 5.
3X = 15 + 5y does not have a single answer. The answer forms a line on the Cartesian plane. In order to reach a single solution you must have two equations when there are two unknowns.
15 and -5 x + y =10 x - y = 20 So it is eventually discovered that x = 15 and y =-5, if you solve the equations.
The terms consistent and dependent are two ways to describe a system of linear equations. A system of linear equations is dependent if you can algebraically derive one of the equations from one or more of the other equations. A system of linear equations is consistent if they have a common solution.An example of a dependent system of linear equations:2x + 4y = 84x + 8y = 16Solve the first equation for x:x = 4 - 2yPlug that value of x into the second equation:16 - 8y + 8y = 16, which gives 16 = 16.No new information was gained from the second equation, because we already knew 16 = 16, so these two equations are dependent.An example of an inconsistent system of linear equations:Because consistency is boring.2x + 4y = 84x + 8y = 15Solve the first equation for x:x = 4 - 2yPlug that value of x into the second equation:16 - 8y + 8y = 15, which gives 16 = 15.This is a contradiction, because 16 doesn't equal 15. Therefore this system has no solution and is inconsistent.