Brilio.net - Two-Variable Linear Equation System (SLE) is one of the basic concepts in mathematics that is often used in various fields, from economics to engineering. SLE involves two equations, each of which has two variables, usually denoted by x and y. A good understanding of SLE is essential, as this concept is the foundation for many more complex mathematical topics.
When talking about SPLDV, it is not only the theory that is discussed, but also the practical application of this system in everyday life. For example, when calculating the total cost of several items or determining the intersection point between two lines, SPLDV becomes a very useful tool. By learning the right solution method, you will be able to solve various mathematical problems more efficiently and accurately.
In this article, we will discuss several methods of solving SPLDV, such as the substitution and elimination methods, and provide examples of problems complete with steps to solve them. By following this guide, you will be better prepared for exams or assignments related to SPLDV and improve your overall math skills.
The following is a complete review as compiled by brilio.net from various sources, Wednesday (22/1).
Understanding the system of linear equations in two variables (SPLDV)
A System of Linear Equations in Two Variables (SLE) is a set of two linear equations each of which has two variables, usually denoted by x and y.
The general form of SPLDV can be written as:
ax + by = c
dx + ey = f
where a, b, d, and e are coefficients, while c and f are constants. SPLDV is often used in various applications, such as calculating profits, costs, or comparing prices of goods.
SPLDV Solution Method
There are several methods that can be used to solve SPLDV, including:
1. Substitution Method: Replacing one of the variables with a value from another equation.
2. Elimination Method: Eliminate one variable by adding or subtracting both equations.
3. Graphical Method: Describe both equations in graphical form to find the point of intersection.
4. Matrix Method: Using the concept of matrices to solve systems of equations.
SPLDV Sample Questions
Here are some examples of SPLDV questions and their solutions:
Example question 1
Given the equation:
2x + 4y = 28 (1)
3x + 2y = 22 (2)
Solution:
From equation (1), we can simplify it to:
x+2y=14
Then substitute the value of x from (1) into (2):
3(142y)+2y = 22
Solve to get the y value:
426y+2y = 224y = 20y = 5
Substitute again to get the value of x:
x+2(5) = 14x = 4
Example question 2
Given the equation:
x+y = 3 (1)
2x+y = 8 (2)
Solution:
From equation (1), we can express y:
y = 3x
Substitute into equation (2):
2x+(3x) = 8
Solve to get the value of x:
x3 = 8x = 11
Substitute again to get the value of y:
y=311 = 14
Additional Sample Questions
1. It is known:
xy = 1 and x+y = 5
Answer:
x=3,y=2
2. It is known:
2x+y = 1 and x+y = 3
Answer:
x = 4,y = 1.