To solve a system of equations by addition or subtraction (or elimination), you must eliminate one of the variables so that you could solve for one of the variables. First, in this equation, you must look for a way to eliminate a variable (line the equations up vertically and look to see if there are any numbers that are equal to each other). If there is lets say a –2y on the top equation and a –2y on the bottom equation you could subtract them and they would eliminate themselves by equaling zero. However, this equation does not have any equal terms. So instead we will multiply one or both equations by a number so that they will equal each other resulting in elimination. In this equation we will want to manipulate both equations so that the y’s will both equal –6 (I chose –6 because it is a common term among –2 and –3). Multiply the WHOLE top equation by 3 to equal –6y (you have to multiply 7, -2, and 4 by 3. The outcome of the other two numbers will not matter to the overall equation.) Then multiply the bottom by 2 to equal –6 as well. Again, you have to multiply 2 to the WHOLE equation. Once you finish manipulating the equations you can now eliminate the y variable and only solve for x. If you subtract the -6y’s you must subtract the other numbers from each other as well. After you solve for x, plug it in to any one equation and then solve for y.

...Solvingsystems of linear equations
7.1 Introduction
Let a system of linear equations of the following form:
a11 x1
a21 x1
a12 x2
a22 x2
ai1x1 ai 2 x2
am1 x1 am2 x2
a1n xn
a2 n x n
ain xn
amn xn
b1
b2
bi
bm
(7.1)
be considered, where x1 , x2 , ... , xn are the unknowns, elements aik (i = 1, 2, ..., m;
k =...

...Doctor Gary Hall
Differential Equations
March 2013
Differential Equations in Mechanical Engineering
Often times college students question the courses they are required to take and the relevance they have to their intended career. As engineers and scientists we are taught, and even “wired” in a way, to question things through-out our lives. We question the way things work, such as the way the shocks in our car work to give us a smooth ride back and forth to...

...Solving Exponential and Logarithmic Equations
Exponential Equations (variable in exponent position)
1. Isolate the exponential portion ( base exp onent ): Move all non-exponential factors or terms to the other side of the equation. 2. Take ln or log of each side of the equation. • Make sure to use ln if the base is “e”. Then remember that ln e = 1 . • Make sure to use log if the base is 10. • If the base is neither “e”...

...-------------------------------------------------
Equations and Problem-Solving
* An airplane accelerates down a runway at 3.20 m/s2 for 32.8 s until is finally lifts off the ground. Determine the distance travelled before take-off.
-------------------------------------------------
Solutions
Given: a = +3.2 m/s2 | t = 32.8 s | vi = 0 m/s |
| Find:d = ?? |
d = VI*t + 0.5*a*t2
d = (0 m/s)*(32.8 s) + 0.5*(3.20 m/s2)*(32.8 s)2
d = 1720 m...

...SYSTEM OF LINEAR EQUATIONS IN TWO VARIABLES Solve the following systems: 1.
x y 8 x y 2
by graphing
by substitution
by elimination
by Cramer’s rule
2.
2 x 5 y 9 0 x 3y 1 0
by graphing
by substitution
by elimination
by Cramer’s rule
3.
4 x 5 y 7 0 2 x 3 y 11 0
by graphing
by substitution
by elimination
by Cramer’s rule...

...1. Which equation below represents the quadratic formula?
*a. -b±b2-4ac2a = x
b. a2+b2=c2
c. fx=a0+n=1∞ancosnπxL+bnsinnπxL
2. Which of the following represents a set of parallel lines?
a. Option one
b. Option two
*c. Option three
3. What is the definition of an obtuse angle?
*a. an angle greater than 90°
b. an angle equal to 90°
c. an angle less than 90°
4. Which formula below represents the area of a circle?
a. A=2πr
*b....

...While the ultimate goal is the same, to determine the value(s) that hold true for the equation, solving quadratic equations requires much more than simply isolating the variable, as is required in solving linear equations. This piece will outline the different types of quadratic equations, strategies for solving each type, as well as other methods of solutions such as Completing the Square and...

...Kuta Software - Infinite Algebra 1
Name___________________________________
Systems of Equations Word Problems
Date________________ Period____
1) Find the value of two numbers if their sum is 12 and their difference is 4.
2) The difference of two numbers is 3. Their sum is 13. Find the numbers.
3) Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip the plane only
averaged 112 km/h while flying back into the same wind. Find the speed...

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