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.

Practice Linear Equations in Two Variables

Exercise #1

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 #2

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 #3

Solve the following system of equations:

{xy=52x3y=8 \begin{cases} x-y=5 \\ 2x-3y=8 \end{cases}

Video Solution

Answer

x=2,y=3 x=2,y=-3

Exercise #4

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

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

(II)x4y=8 (II)x-4y=8

Video Solution

Answer

x=8,y=4 x=-8,y=-4

Exercise #5

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

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

(II)6x8y=10 (II)6x-8y=10

Video Solution

Answer

x=4,y=414 x=-4,y=-4\frac{1}{4}

Exercise #1

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

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

(II)2x3and=15 (II)2x-3and=-15

Video Solution

Answer

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

Exercise #2

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

(I)x2and=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 #3

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 #4

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

(I)7x4y=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 #5

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 #1

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 #2

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 #3

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

(I)13x4y=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 #4

Solve the following system of equations:

{2x15y=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 #5

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

(I)4x+4and=15 (I)-4x+4and=15

(II)2x+8and=12 (II)2x+8and=12

Video Solution

Answer

x=95,y=3920 x=-\frac{9}{5},y=\frac{39}{20}