# Linear equation with two variables

πPractice a linear equation with two unknowns

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?

1. 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.
2. 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.

## Test yourself on a linear equation with two unknowns!

$$x+y=8$$

$$x-y=6$$

Example of a solution for a linear equation with two variables:
$x+6y=12$
Let's isolate the $X$
$βββββββx=12-6y$
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.

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## Examples and exercises with solutions of linear equation with two variables

### Exercise #1

$x+y=8$

$x-y=6$

### Video Solution

$x=7,y=1$

### Exercise #2

$3x-y=5$

$5x+2y=12$

### Video Solution

$x=2,y=1$

### Exercise #3

$6x+y=12$

$3y+2x=20$

### Video Solution

$x=1,y=6$

### Exercise #4

$6x+4y=18$

$-2x+3y=20$

### Video Solution

$x=-1,y=6$

### Exercise #5

$-x+y=14$

$5x+2y=7$

### Video Solution

$x=-3,y=11$