System of linear equations - Examples, Exercises and Solutions

Practice Two linear equations with two unknownsPractice Algebraic solution for linear equations with two unknownsPractice Substitution method for two linear equations with two unknownsPractice Solving with the method of equalization for systems of two linear equations with two unknownsPractice Linear equation with two variablesPractice Solving a System of Linear Equations with Two Variables Using Algebraic Method
Question Types:
Algebraic Solution: Solving an equation by adding/subtracting from both sidesAlgebraic Solution: Solve using the substitution method

A linear equation is an equation of the type:
y=ax+by=ax+b

A system of two linear equations with two unknowns is a pair of adjacent linear equations or written one below the other, either within braces or without graphic signs.

A system of two linear equations

To solve a system of equations, several steps must be taken:

  • Isolate the variables in all the equations.
  • Place possible values to the isolated variables (for example Y=0,1,2Y=0,1,2.
  • Compare two equations (it is advisable to illustrate them on a graph).
  • Find the point of intersection of the two equations.
Detailed explanation

Practice System of linear equations

Question 1

Solve the following system of equations:

\( \begin{cases} x-y=5 \\ 2x-3y=8 \end{cases} \)

Question 2

Solve the above set of equations and choose the correct answer.

\( \begin{cases} -5x+4y=3 \\ 6x-8y=10 \end{cases} \)

Question 3

Solve the above set of equations and choose the correct answer.

\( \begin{cases} -2x+3y=4 \\ x-4y=8 \end{cases} \)

Question 4

Solve the following equations:

\( \begin{cases} 2x+y=9 \\ x=5 \end{cases} \)

Question 5

Solve the following equations:

\( \begin{cases} x+y=18 \\ y=13 \end{cases} \)

Examples with solutions for System of linear equations

Exercise #1

Solve the following system of equations:

{x−y=52x−3y=8 \begin{cases} x-y=5 \\ 2x-3y=8 \end{cases}

Video Solution

Answer

x=7,y=2 x=7,y=2

Exercise #2

Solve the above set of equations and choose the correct answer.

{−5x+4y=36x−8y=10 \begin{cases} -5x+4y=3 \\ 6x-8y=10 \end{cases}

Video Solution

Answer

x=−4,y=−414 x=-4,y=-4\frac{1}{4}

Exercise #3

Solve the above set of equations and choose the correct answer.

{−2x+3y=4x−4y=8 \begin{cases} -2x+3y=4 \\ x-4y=8 \end{cases}

Video Solution

Answer

x=−8,y=−4 x=-8,y=-4

Exercise #4

Solve the following equations:

{2x+y=9x=5 \begin{cases} 2x+y=9 \\ x=5 \end{cases}

Video Solution

Answer

x=5,y=−1 x=5,y=-1

Exercise #5

Solve the following equations:

{x+y=18y=13 \begin{cases} x+y=18 \\ y=13 \end{cases}

Video Solution

Answer

x=5,y=13 x=5,y=13

Question 1

Solve the following system of equations:

\( \begin{cases} -8x+5y=3 \\ 10x+y=16 \end{cases} \)

Question 2

Solve the above set of equations and choose the correct answer.

\( \begin{cases} 7x-4y=8 \\ x+5y=12.8 \end{cases} \)

Question 3

Solve the above set of equations and choose the correct answer.

\( \begin{cases} -8x+3y=7 \\ 24x+y=3 \end{cases} \)

Question 4

Find the value of x and and band the substitution method.

\( \begin{cases} -x-2y=4 \\ 3x+y=8 \end{cases} \)

Question 5

Find the value of x and and band the substitution method.

\( \begin{cases} x+y=5 \\ 2x-3y=-15 \end{cases} \)

Exercise #6

Solve the following system of equations:

{−8x+5y=310x+y=16 \begin{cases} -8x+5y=3 \\ 10x+y=16 \end{cases}

Video Solution

Answer

x=1.32,y=2.8 x=1.32,y=2.8

Exercise #7

Solve the above set of equations and choose the correct answer.

{7x−4y=8x+5y=12.8 \begin{cases} 7x-4y=8 \\ x+5y=12.8 \end{cases}

Video Solution

Answer

x=2.33,y=2.09 x=2.33,y=2.09

Exercise #8

Solve the above set of equations and choose the correct answer.

{−8x+3y=724x+y=3 \begin{cases} -8x+3y=7 \\ 24x+y=3 \end{cases}

Video Solution

Answer

x=0.025,y=2.4 x=0.025,y=2.4

Exercise #9

Find the value of x and and band the substitution method.

{−x−2y=43x+y=8 \begin{cases} -x-2y=4 \\ 3x+y=8 \end{cases}

Video Solution

Answer

x=4,y=−4 x=4,y=-4

Exercise #10

Find the value of x and and band the substitution method.

{x+y=52x−3y=−15 \begin{cases} x+y=5 \\ 2x-3y=-15 \end{cases}

Video Solution

Answer

x=0,y=5 x=0,y=5

Question 1

Solve the following system of equations:

\( \begin{cases} 2x-\frac{1}{5}y=18 \\ 3x+y=6 \end{cases} \)

Question 2

Solve the above set of equations and choose the correct answer.

\( \begin{cases} \frac{1}{3}x-4y=5 \\ x+6y=9 \end{cases} \)

Question 3

Find the value of x and and band the substitution method.

\( \begin{cases} -5x+9y=18 \\ x+8y=16 \end{cases} \)

Question 4

Find the value of x and and band the substitution method.

\( (I)-x+3and=12 \)

\( (II)4x+2and=10 \)

Question 5

Solve the above set of equations and choose the correct answer.

\( \begin{cases} \frac{1}{2}x+\frac{7}{2}y=10 \\ -3x+7y=12 \end{cases} \)

Exercise #11

Solve the following system of equations:

{2x−15y=183x+y=6 \begin{cases} 2x-\frac{1}{5}y=18 \\ 3x+y=6 \end{cases}

Video Solution

Answer

x=7.38,y=−16.14 x=7.38,y=-16.14

Exercise #12

Solve the above set of equations and choose the correct answer.

{13x−4y=5x+6y=9 \begin{cases} \frac{1}{3}x-4y=5 \\ x+6y=9 \end{cases}

Video Solution

Answer

x=11,y=−13 x=11,y=-\frac{1}{3}

Exercise #13

Find the value of x and and band the substitution method.

{−5x+9y=18x+8y=16 \begin{cases} -5x+9y=18 \\ x+8y=16 \end{cases}

Video Solution

Answer

x=0,y=2 x=0,y=2

Exercise #14

Find the value of x and and band the substitution method.

(I)−x+3and=12 (I)-x+3and=12

(II)4x+2and=10 (II)4x+2and=10

Video Solution

Answer

x=37,y=297 x=\frac{3}{7},y=\frac{29}{7}

Exercise #15

Solve the above set of equations and choose the correct answer.

{12x+72y=10−3x+7y=12 \begin{cases} \frac{1}{2}x+\frac{7}{2}y=10 \\ -3x+7y=12 \end{cases}

Video Solution

Answer

x=2,y=2.57 x=2,y=2.57