Systems of Linear Equations

Solving Systems of Linear Equations

It is a set of linear equations with the same unknown variables

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​A System of Linear Equations

There are three types of solutions:

a) Infinite solutions

b) One solution

c) No solution​

Types of solutions

Solving methods

• Substitution

• Elimination

Algebra Methods

Graphing

Solution at the point

(1, 5)

x= 1, y =5

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Graphing Method

Fill in the Blank

Give the coordinates of the solution of the system shown

Fill in the Blank

What is the solution? 

(Write your answer as a coordinate, infinite solution or no solution)

Multiple Choice

How many solutions does this system of equations have?

• One Solution

• No solution

• Infinitely Many Solutions

• Two Solutions

Fill in the Blank

Give the coordinates of the solution of the system shown

(Write your answer as a coordinate, infinite solution or no solution)

Multiple Choice

If a system of equations has no solution, what does the graph look like? 

• intersecting lines

• parallel lines

• skew lines

• intersecting lines

Fill in the Blank

Solve the system of equations by graphing.

(Write your answer as a coordinate, infinite solution or no solution)

Multiple Choice

How many solutions will this system have? 

• No solution

• One Solution

• I Don't Know

• Infinitely Many Solutions

We solve for one variable and substitute it in the opposite equation.

​Substitution

The aim is to eliminate one variable from the system.

We solve the equation for one variable and substitute it to find the other value

​Elimination

Algebra Methods

1. Find the best variable to eliminate

2. Multiply any equation by the most suitable number

3. Add the equations

4. Solve for the variable

5. Use your value to find the missing one

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Elimination

Method

Multiple Choice

Which variable is the easiest to eliminate in this system? 

3x - 2y = 12

2x + 2y = - 2

• x

• y

• both

• neither

Multiple Choice

Which variable is the easiest to eliminate in this system? 

   3x + 5y = - 15

 - 3x - 4y = 30  

• x

• y

• both

• neither

Multiple Choice

What would be the first step in solving this system using the Elimination Method?

2x + 2y = -2

3x - 2y = 12

• You cannot solve this using the Elimination Method.

• Cross out the 2x and 3x

• Add the like terms. The y terms will cancel out.

• Change to slope intercept form and graph

Solve by elimination

Solve by elimination

Fill in the Blank

Solve the system by elimination.

x + 6y = 17

x - 3y = 8

(Write your answer as a coordinate, infinite solution or no solution)

Fill in the Blank

Solve the system by elimination

3x + y = 19

2x - y = 6

(Write your answer as a coordinate, infinite solution or no solution)

1. Find the best variable to solve for

2. Substitute the expression in the opposite equation and solve for the remaining variable

3. Use the value to find the missing one

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Substitution

Method

Multiple Choice

Which equation is easier to solve for y variable.

• 1st

• 2nd

Multiple Choice

Write the new equation to solve after using the substitution process correctly for the system.

y = 5x - 7

-3x - 2y= -12

• -3(5x - 7) - 2y= -12

• -3x - 2(5x-7) = -12

• -3x -2y = 12(5x-7)

Solve by substitution

Solve by substitution

Fill in the Blank

Solve the system of equations by substitution. y = -4x + 5 y =  3x - 16

(Write your answer as a coordinate, infinite solution or no solution)

Fill in the Blank

Solve the system of equations using substitution: -4x + 4y = 8 y = -2x - 10

(Write your answer as a coordinate, infinite solution or no solution)