Substitution method for two linear equations with two unknowns - Examples, Exercises and Solutions

Question Types:
Algebraic Solution: Solving an equation by adding/subtracting from both sidesAlgebraic Solution: Solve using the substitution method

To solve with the substitution method a system of two linear equations with two unknowns we will have to substitute one of the unknowns in some equation and thus obtain an equation with only one unknown.

How do we do it?

  • Choose the equation in which you can easily isolate one of the unknowns (isolate it in such a way that it cannot express itself).
  • Put the unknown that you have isolated in the second equation of the system: you will have an equation with one unknown and you will discover the value of the first one.
  • Go back to the system of equations and place the value of the unknown you found in one of the equations or in the equation obtained to find the second unknown.
Detailed explanation

Suggested Topics to Practice in Advance

  1. Linear equation with two variables

Practice Substitution method for two linear equations with two unknowns

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.

\( (I)-5x+4y=3 \)

\( (II)6x-8y=10 \)

Question 3

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

\( (I)-2x+3y=4 \)

\( (II)x-4y=8 \)

Question 4

Solve the following equations:

\( (I)2x+y=9 \)

\( (II)x=5 \)

Question 5

Solve the following equations:

\( (I)x+y=18 \)

\( (II)y=13 \)

Examples with solutions for Substitution method for two linear equations with two unknowns

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=2,y=−3 x=2,y=-3

Exercise #2

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

(I)−5x+4y=3 (I)-5x+4y=3

(II)6x−8y=10 (II)6x-8y=10

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.

(I)−2x+3y=4 (I)-2x+3y=4

(II)x−4y=8 (II)x-4y=8

Video Solution

Answer

x=−8,y=−4 x=-8,y=-4

Exercise #4

Solve the following equations:

(I)2x+y=9 (I)2x+y=9

(II)x=5 (II)x=5

Video Solution

Answer

x=5,y=−1 x=5,y=-1

Exercise #5

Solve the following equations:

(I)x+y=18 (I)x+y=18

(II)y=13 (II)y=13

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.

\( (I)7x-4y=8 \)

\( (II)x+5y=12.8 \)

Question 3

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

\( (I)-8x+3y=7 \)

\( (II)24x+y=3 \)

Question 4

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

\( (I)-x-2and=4 \)

\( (II)3x+and=8 \)

Question 5

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

\( (I)x+and=5 \)

\( (II)2x-3and=-15 \)

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.

(I)7x−4y=8 (I)7x-4y=8

(II)x+5y=12.8 (II)x+5y=12.8

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.

(I)−8x+3y=7 (I)-8x+3y=7

(II)24x+y=3 (II)24x+y=3

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.

(I)−x−2and=4 (I)-x-2and=4

(II)3x+and=8 (II)3x+and=8

Video Solution

Answer

x=4,y=−4 x=4,y=-4

Exercise #10

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

(I)x+and=5 (I)x+and=5

(II)2x−3and=−15 (II)2x-3and=-15

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.

\( (I)\frac{1}{3}x-4y=5 \)

\( (II)x+6y=9 \)

Question 3

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

\( (I)-5x+9and=18 \)

\( (II)x+8and=16 \)

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.

\( (I)\frac{1}{2}x+\frac{7}{2}y=10 \)

\( (II)-3x+7y=12 \)

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.

(I)13x−4y=5 (I)\frac{1}{3}x-4y=5

(II)x+6y=9 (II)x+6y=9

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.

(I)−5x+9and=18 (I)-5x+9and=18

(II)x+8and=16 (II)x+8and=16

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.

(I)12x+72y=10 (I)\frac{1}{2}x+\frac{7}{2}y=10

(II)−3x+7y=12 (II)-3x+7y=12

Video Solution

Answer

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

Topics learned in later sections

  1. Two linear equations with two unknowns
  2. Algebraic solution for linear equations with two unknowns
  3. Solving with the method of equalization for systems of two linear equations with two unknowns