Illustrating Systems of Linear Equation

Illustrating systems of linear equation

By Rose Lutrania

Multiple Choice

Which of the following equations is linear?

• x²+3x= 5

• 3x+5y= 20

• y³+ y=-9

• x+y²=1

Multiple Choice

The following are examples of system of linear equations in two variable EXCEPT______.

• 2x+3y=2

  x-y=5

• x+ y=-9

  3x+ 6y=-2

• 5a²+ b=-9

  3a²-b=10

  2a=20

• x+y=23

  y=2x

Fill in the Blanks

It consists of two or more linear equations in two variables.

1​Determine whether point (– 3, 1) is a solution of the system

x – y = – 4  

2x + 10y = 4

​Determine whether the given point is

a solution of the following system

  point:  (4, 2)

  system:  2x – 5y = – 2 

3x + 4y = 4

Subject | Subject

Some text here about the topic of discussion

​Identify the system, the no. of solution and graph of the following systems.

​1. 2x+y=15

3x−y=5

​3. 2x + y = 0  

y = –2x + 1

2​. 3x + y =0  

  2y= –6x

​Type	​	​	​
​Solution	​	​	​
​Graph	​	​	​

Multiple Choice

How many solutions do we have in an inconsistent system?

• 1

• 2

• 0

• Many or infinite

Multiple Choice

What is the graph of a system with many solutions?

• intersecting lines

• parallel lines

• overlapping

• skew lines

Multiple Choice

What type of system is present if the graph is intersecting?

• consistent/ Dependent system

• Inconsistent

• Consistent/Independent System

Multiple Choice

How many solution/s can we find if the graph of the system are intersecting lines?

• 1

• 2

• 0

• Infinite/Many

​

Solving a System of Linear Equations by the Substitution Method

​

1)Solve one of the equations for a variable.

2)Substitute the expression from step 1 into the other equation.

3)Solve the new equation.

4)Substitute the value found in step 3 into either equation containing both variables.

5)Check the proposed solution in the original equations.

​Solve by substitution method

y = -6

-3x - 6y = 24​

Multiple Choice

Solve using substitution method

8x + y = 12

y = x + 3​

• (1, 4)

• 2

• (4,1)

Solving a System of Linear Equations by the Addition or Elimination Method

1Rewrite each equation in standard form, eliminating fraction coefficients.

2)If necessary, multiply one or both equations by a number so that the coefficients of a chosen variable are opposites.

3)Add the equations.

4)Find the value of one variable by solving equation from step 3.

5)Find the value of the second variable by substituting the value found in step 4 into either original equation.

Check the proposed solution in the original equations.

Multiple Choice

Solve:

x = -3y - 17

2x + 3y = -7

• (1, -20)

• (-5, -2)

• (3, 0)

• (10 , -9)

Solve using elimination method:

1. x - y = 11

2x + y = 19

Some text here about the topic of discussion

Multiple Choice

4x+ 9y = 28

-4x -y = -28

• (-7,0)

• (7,0)

• (-6,0)

• (6,0)

Multiple Choice

 

Solve the system:

x + 6y = 17

-x + 3y = -8

• (5, 2)

• (1, 11)

• (11, 1)

• no solution