Chapter 6 – Systems of Linear Equations
... 6.2 – Solving systems of 2 equations using the Addition-Subtraction method When a graphing tool is not available, systems of equations can be solved algebraically. Two techniques for doing this are discussed here: 1. Algebraically solving the system using the Addition-Subtraction method 2. Algebrai ...
... 6.2 – Solving systems of 2 equations using the Addition-Subtraction method When a graphing tool is not available, systems of equations can be solved algebraically. Two techniques for doing this are discussed here: 1. Algebraically solving the system using the Addition-Subtraction method 2. Algebrai ...
Systems of Linear Equations Math 130 Linear Algebra
... You already know how to solve systems of linear equations, and we’ve looked at the ancient Chinese method of elimination to solve them. We’ll analyze that algorithm and introduce some terminology associated with it. Although we’ll have a lot more use for matrices later, for the time being we’ll use ...
... You already know how to solve systems of linear equations, and we’ve looked at the ancient Chinese method of elimination to solve them. We’ll analyze that algorithm and introduce some terminology associated with it. Although we’ll have a lot more use for matrices later, for the time being we’ll use ...
Math 60 Test # 2 Fall 2014
... 11. Solve for x: (10 pts) x/3 < x/2 + 1< 2x Break into two inequalities: x/3 < x/2 + 1 and x/2 + 1 < 2x For the first, multiply by 6 2x < 3x + 6, or x > -6; if you got to –x < 6, you needed to change the orientation if you divided by a negative number. ...
... 11. Solve for x: (10 pts) x/3 < x/2 + 1< 2x Break into two inequalities: x/3 < x/2 + 1 and x/2 + 1 < 2x For the first, multiply by 6 2x < 3x + 6, or x > -6; if you got to –x < 6, you needed to change the orientation if you divided by a negative number. ...
solutions for the practice test
... (3) Draw a diagram of which points in the plane satisfy the inequality 2(x + y) > 3x − y + 6. First, let’s put the inequality into slope-intercept form: 2(x + y) > 3x − y + 6 2x + 2y > 3x − y + 6 2x + 3y > 3x + 6 3y > x + 6 y > 13 x + 2. So the boundary line is y = 13 x + 2. The boundary line does n ...
... (3) Draw a diagram of which points in the plane satisfy the inequality 2(x + y) > 3x − y + 6. First, let’s put the inequality into slope-intercept form: 2(x + y) > 3x − y + 6 2x + 2y > 3x − y + 6 2x + 3y > 3x + 6 3y > x + 6 y > 13 x + 2. So the boundary line is y = 13 x + 2. The boundary line does n ...
Equation
In mathematics, an equation is an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions. An equation differs from an identity in that an equation is not necessarily true for all possible values of the variable.There are many types of equations, and they are found in all areas of mathematics; the techniques used to examine them differ according to their type.Algebra studies two main families of equations: polynomial equations and, among them, linear equations. Polynomial equations have the form P(X) = 0, where P is a polynomial. Linear equations have the form a(x) + b = 0, where a is a linear function and b is a vector. To solve them, one uses algorithmic or geometric techniques, coming from linear algebra or mathematical analysis. Changing the domain of a function can change the problem considerably. Algebra also studies Diophantine equations where the coefficients and solutions are integers. The techniques used are different and come from number theory. These equations are difficult in general; one often searches just to find the existence or absence of a solution, and, if they exist, to count the number of solutions.Geometry uses equations to describe geometric figures. The objective is now different, as equations are used to describe geometric properties. In this context, there are two large families of equations, Cartesian equations and parametric equations.Differential equations are equations involving one or more functions and their derivatives. They are solved by finding an expression for the function that does not involve derivatives. Differential equations are used to model real-life processes in areas such as physics, chemistry, biology, and economics.The ""="" symbol was invented by Robert Recorde (1510–1558), who considered that nothing could be more equal than parallel straight lines with the same length.