Solve the following system of equations: $ \begin{cases} x+y=8 \\ x=5-y \end{cases} $

There are infinite solutions.

Solve the following system of equations: $ \begin{cases} 5x-y=0 \\ 10x-2y=0 \end{cases} $

There are infinite solutions.

Linear equation with two variables

An equation that has two variables: $X$ and $Y$ .
$y=a\times x+b$
To solve a linear equation that has two variables, we must find a pair of values for $X$ and for $Y$ that preserve the equation.
How will we do it?

Try to isolate one variable, whichever you prefer, then leave it alone on one side so that it does not have a value by itself.
Place any number you want instead of the variable you have not isolated and discover the value of the isolated variable.

In this way, you will be able to discover the pair of variables that satisfy the equation in question.

This type of equations generally has infinite solutions.
If you create a value table for this equation and treat it as a function, you can plot it on the Cartesian plane and see what it looks like graphically.

Detailed explanation

Start practice

Test yourself on a linear equation with two unknowns!

$$ x+y=8 $$

$$ x-y=6 $$

Practice more now

Example of a solution for a linear equation with two variables:
$x+6y=12$
Let's isolate the $X$
$x=12-6y$
Let's substitute any number for $Y$ , for example and find out the $X$ :
$y=4$
$x=12-6\times4$

$x=-12$
Notice that the result obtained is correct $x=-12, y=4$ ,
but, this is one among the infinite possible solutions for this equation.

If you are interested in this article, you might also be interested in the following articles

Variables and Algebraic Expressions
First Degree Equations with One Variable
What is the Variable of a Mathematical Equation?
System of Two Linear Equations with Two Variables
Graphical Method Solution for a System of Linear Equations with Two Variables
Algebraic Solution for a System of Linear Equations with Two Variables
Solution with the Substitution Method for Systems of Two Linear Equations with Two Variables
Solution with the Equalization Method for Systems of Two Linear Equations with Two Variables
Solving Verbal Problems with a System of Linear Equations

In the Tutorela blog, you will find a wide variety of mathematics articles