# How To Solve Problems Algebraically Then there’s a whole bunch of problems (used primarily in engineering, but I’m sure they sometimes interest mathematicians) that can’t be integrated/solved/etc directly, and so require either approximations or look-up tables (which are generally categorized as “brute force” methods). There’s some calculus or geometry or trig problems that can only be approximated algebraically.Then, see how find the value of that variable and use it to find the value of the other variable. There are many different ways to solve a system of linear equations.

You can use the substitution method even if both equations of the linear system are in standard form.

Just begin by solving one of the equations for one of its variables.

Break the problem down into smaller bits and solve each bit at a time.

First, we need to translate the word problem into equation(s) with variables.

$$y=2x 4$$ $$3x y=9$$ We can substitute y in the second equation with the first equation since y = y.

in the first equation $$y=2x 4$$ $$y=2\cdot 4$$ $$y=6$$ The solution of the linear system is (1, 6).Then, the further you get into engineering and away from pure math, the more of these you run into, including math problems that involve large angle deflections or material properties or thermal properties or anything else that is very complex/requires approximations or lookup tables.Large angle deflections of continuous materials (such as compliant mechanisms) can be written as math problems that either have to be approximated or require some sort of lookup table. Take one of the equations and solve it for one of the variables.Then plug that into the other equation and solve for the variable.Let's try θ = 30°: sin(−30°) = −0.5 and −sin(30°) = −0.5 So it is true for θ = 30° Let's try θ = 90°: sin(−90°) = −1 and −sin(90°) = −1 So it is also true for θ = 90° Is it true for all values of θ? $x y=9$$x \left ( \right )=9$$$x 4=9$$x=5$$ $$x=1$$ This value of x can then be used to find y by substituting 1 with x e.g.Coin Problems deal with items with denominated values.Similar word problems are Stamp Problems and Ticket Problems.Consecutive Integer Problems deal with consecutive numbers.The number sequences may be Even or Odd, or some other simple number sequences.

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