# A linear equation with two unknowns - Examples, Exercises and Solutions

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.

## Practice A linear equation with two unknowns

### Exercise #1

$x+y=8$

$x-y=6$

### Answer

$x=7,y=1$

### Exercise #2

$3x-y=5$

$5x+2y=12$

### Answer

$x=2,y=1$

### Exercise #3

$6x+y=12$

$3y+2x=20$

### Answer

$x=1,y=6$

### Exercise #4

$6x+4y=18$

$-2x+3y=20$

### Answer

$x=-1,y=6$

### Exercise #5

$-x+y=14$

$5x+2y=7$

### Answer

$x=-3,y=11$

### Exercise #1

Solve the following system of equations:

$\begin{cases} x+y=8 \\ x=5-y \end{cases}$

### Answer

There is no solution.

### Exercise #2

$x-y=8$

$2x-2y=16$

### Answer

Infinite solutions

### Exercise #3

$4x-8y=16$

$-x-2y=24$

### Answer

$x=-10,y=-7$

### Exercise #4

$6x-2y=24$

$x+5y=4$

### Answer

$x=4,y=0$

### Exercise #5

$4x+3y=-11$

$3x-2y=-4$

### Answer

$x=-2,y=-1$

### Exercise #1

$x-y=8$

$3x+2y=24$

### Answer

$x=8,y=0$

### Exercise #2

$5y+3x=15$

$-2y-4x=-34$

### Answer

$x=10,y=-3$

### Exercise #3

Solve the following system of equations:

$\begin{cases} 5x-y=0 \\ 10x-2y=0 \end{cases}$

### Answer

There are infinite solutions.

### Exercise #4

$x+y=0$

$x+y=10$

No solution

### Exercise #5

$2x-2y=10$

$4x-4y=32$

No solution