Algebraic Solution - Examples, Exercises and Solutions

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

A system of linear equations is, in fact, a set of conditions that must be satisfied by specific unknowns,
the solution for the system of equations is then based on finding the X X and the Y Y that agree with both the first equation and the second equation.

These questions can be solved in several ways, the algebraicsolution includes two methods:

Substitution method:

  1. Isolate an unknown in any of the equations.
  2. Substitute the unknown we isolated in the other equation of the system and find the value of an unknown.
  3. We place the value of the unknown that we have discovered in one equation to find the value of the other.

Step-by-step solution of a system of linear equations with two variables: 2X + Y = 5 and 2X + Y = 3. The solution involves elimination to find Y = 2, substitution to solve for X = 1.5, and clear visual formatting for educational clarity. Featured in a guide on solving linear systems algebraically.

Equalization method

  1. We will cause the coefficients in both equations (X X or Y Y ) to become equal.
  2. We will add or subtract one equation from the other and thus eliminate the equal coefficients.
  3. We will solve the equation with the isolated coefficient and find its value.
  4. We place the value of the unknown that we have discovered in one equation to find the value of the other.

Step-by-step solution of a system of linear equations with two variables using substitution: 2X - Y = 5 and 2X + Y = 3. The solution involves isolating Y, substituting into the second equation to find X = 2, and then substituting back to find Y = -1. Featured in a guide on solving linear systems algebraically with substitution.

Detailed explanation

Suggested Topics to Practice in Advance

  1. Linear equation with two variables

Practice Algebraic Solution

Question 1

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

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

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

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 following equations:

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

\( (II)x=5 \)

Question 4

Solve the following equations:

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

\( (II)y=13 \)

Question 5

Solve the following system of equations:

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

Examples with solutions for Algebraic Solution

Exercise #1

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 #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 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 #4

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

Exercise #5

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

Question 1

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

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

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

Question 2

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

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

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

Question 3

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

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

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

Question 4

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

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

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

Question 5

Solve the following system of equations:

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

Exercise #6

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 #7

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

Exercise #8

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 #9

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 #10

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

Question 1

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

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

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

Question 2

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

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

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

Question 3

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

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

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

Question 4

Solve the following system of equations:

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

Question 5

Choose the correct answer for the following exercise:

\( (I)x+y=15 \)

\( (II)2x+2y=12\frac{}{} \)

Exercise #11

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 #12

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 #13

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 #14

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 #15

Choose the correct answer for the following exercise:

(I)x+y=15 (I)x+y=15

(II)2x+2y=12 (II)2x+2y=12\frac{}{}

Video Solution

Answer

No solution

Topics learned in later sections

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