How do you write a system of linear equations in two variables? Explain this in words and by using mathematical notation in an equation.
To write a system of linear equations in two variables, you need two equations that involve the same two variables. The idea is to find the values of the variables that satisfy both equations simultaneously.
First, let's denote the two variables as x and y. The general form of a linear equation in two variables is written as:
ax + by = c
where a, b, and c are constants.
Let's consider an example to better understand this. Suppose we have the following two equations:
2x + 3y = 7 (Equation 1)
4x - y = 5 (Equation 2)
Now, we have a system of linear equations with two variables: x and y.
We can write this system of equations using mathematical notation as:
{ 2x + 3y = 7
{ 4x - y = 5
The curly braces indicate that these two equations are being considered as a system.
By solving this system, we aim to find the values of x and y that satisfy both equations simultaneously. This means that when we substitute these values back into the equations, both equations will hold true.
Once we have the system written, we can use different methods, such as substitution, elimination, or matrices, to solve for the values of x and y. The solution to the system will be the values of x and y that satisfy both equations.