As a retired teacher of mathematics, this question made me smile!
As I often told my middle school students, "You will, probably, only need 10% of the mathematics we teach, in school, to be successful in life. However, only your life can tell you which 10%."
Having said this, linear equations:
1) Would enable you to determine where two lines intersect. (Useful in construction)
2) Find the break even point in marketing.
3) Determine how long it would take to reach almost any goal that could be expressed as a time dependent equation.
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When solving equations remember that whatever operations are performed on the LHS of the equation must be performed on its RHS to keep the equation in balance.
Why? - Mainly to help in solving equations.
Non-linear partial differential equations. Are you offering to help me? If not, why did you ask?
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.
if you are good at math, you would know. I'm not being mean, but sometimes it takes a little help from an adult.