What is linear equation? Let’s learn about it!
To begin, let us start with a question; What is a linear equation? As per the linear equation definition, linear equations constitutes any algebraic equation with power of one. The common form of linear equation is y = ax + b. Here a and b are constants while x and y are variables. When plotted in the plane, they form a straight line and hence they are called linear. As per the definition of linear equations, they can be expressed in any of the format given below.
Standard Format: ax + by +c =0, where a, b and c are constants.
Slope-Intercept Format: y = mx + b. Here m being the slope of line and b is its y-intercept.
Point Slope Format: (y – y1) = a(x – x1). Here a, x1 and y1 are constants.
Intercept Format: x/a + y/b = 1.
This are some of the commonly used formats. They provide solution only to a single linear equation. While the systems of linear equations can be used for solving set of equations.
Solving systems of linear equations:
A system of linear equations contain number of linear equations that can be solved together. Say for example, a1x + b1y + c1z = d1, a2x + b2y + c2z = d2 and a3x + b3y + c3z = d3 are system of linear equations with 3 variables x,y and z. To solve them , The number of equations should be equal or more than the number of variables. Let us solve linear equation word problems and get practical idea of the topic.
Solving linear equation word problems:
Let us solve word problems to gain deep knowledge of the subject.
(i) The sum of the age of John and Michelle is 13 while product is 40. If John is older than Michelle, find their respective ages?
Let age of John be x while that of Michelle be y, than we have x + y = 13 and x * y = 40 or y = 40/x. Substituting this value in first equation, x + 40/x =13 or x2 – 13x + 40 = 0. Factorizing it, (x – 8)(x – 5) = 0 i.e. x = 8 or x = 5. But since John is older, x = 8 and y = 5. Thus John is 8 years older while Michelle is 5 years old.
Solving linear equations problems:
Now that we have solved word problem and understood what are linear equations, lets solve simple linear equations problems.
(i) Solve for a and b, 3a + 2b = 4 and 2a + 3b = 3:
Multiplying 1st equation by 2 and 2nd by 3, 6a + 4b = 8 and 6a + 9b = 9. Subtracting 1st from 2nd, we have 6a + 4b – 6a – 9b = 8 – 9 or -5b = -1 i.e. b = 1/5. Putting this value in 1st equation, 3a + 2/5 = 4 or a = 6/5.
|More topics in Linear Equations|
|Solving Linear Equations||Graphing Linear Equations|
|Linear Equations Examples||Point Slope Form|
|Point Slope Form Examples|
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