Linear Equations with Two Variables - 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?

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.

Practice Linear Equations with Two Variables

Question 1

$$ x+y=8 $$

$$ x-y=6 $$

Question 2

Solve the following system of equations:

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

Question 3

$$ 3x-y=5 $$

$$ 5x+2y=12 $$

Question 4

$$ 6x+y=12 $$

$$ 3y+2x=20 $$

Question 5

$$ 6x+4y=18 $$

$$ -2x+3y=20 $$

Examples with solutions for Linear Equations with Two Variables

Exercise #1

$x+y=8$

$x-y=6$

Video Solution

Answer

$x=7,y=1$

Exercise #2

Solve the following system of equations:

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

Video Solution

Answer

There is no solution.

Exercise #3

$3x-y=5$

$5x+2y=12$

Video Solution

Answer

$x=2,y=1$

Exercise #4

$6x+y=12$

$3y+2x=20$

Video Solution

Answer

$x=1,y=6$

Exercise #5

$6x+4y=18$

$-2x+3y=20$

Video Solution

Answer

$x=-1,y=6$

Question 1

$$ -x+y=14 $$

$$ 5x+2y=7 $$

Question 2

$$ 6x-2y=24 $$

$$ x+5y=4 $$

Question 3

$$ 4x+3y=-11 $$

$$ 3x-2y=-4 $$

Question 4

$$ x-y=8 $$

$$ 3x+2y=24 $$

Question 5

$$ 4x-8y=16 $$

$$ -x-2y=24 $$

Exercise #6

$-x+y=14$

$5x+2y=7$

Video Solution

Answer

$x=-3,y=11$

Exercise #7

$6x-2y=24$

$x+5y=4$

Video Solution

Answer

$x=4,y=0$

Exercise #8

$4x+3y=-11$

$3x-2y=-4$

Video Solution

Answer

$x=-2,y=-1$

Exercise #9

$x-y=8$

$3x+2y=24$

Video Solution

Answer

$x=8,y=0$

Exercise #10

$4x-8y=16$

$-x-2y=24$

Video Solution

Answer

$x=-10,y=-7$

Question 1

$$ x-y=8 $$

$$ 2x-2y=16 $$

Question 2

Solve the following system of equations:

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

Question 3

$$ 5y+3x=15 $$

$$ -2y-4x=-34 $$

Question 4

$$ 2x-2y=10 $$

$$ 4x-4y=32 $$

Question 5

$$ x+y=0 $$

$$ x+y=10 $$

Exercise #11

$x-y=8$

$2x-2y=16$

Video Solution

Answer

Infinite solutions

Exercise #12

Solve the following system of equations:

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

Video Solution

Answer

There are infinite solutions.

Exercise #13

$5y+3x=15$

$-2y-4x=-34$

Video Solution

Answer

$x=10,y=-3$

Exercise #14

$2x-2y=10$

$4x-4y=32$

Video Solution

Answer

No solution

Exercise #15

$x+y=0$

$x+y=10$

Video Solution

Answer

No solution

Topics learned in later sections