Systems of Linear Equations

Presentation

•

Mathematics

•

10th Grade

•

Hard

James Gonzalez

FREE Resource

12 Slides • 16 Questions

Solving Systems of Linear Equations

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

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

Graphing Method

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Multiple Choice

How many solutions does this system of equations have?

One Solution

No solution

Infinitely Many Solutions

Two Solutions

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Multiple Choice

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

intersecting lines

parallel lines

skew lines

intersecting lines

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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

Find the best variable to eliminate
Multiply any equation by the most suitable number
Add the equations
Solve for the variable
Use your value to find the missing one

Elimination

Method

Multiple Choice

Which variable is the easiest to eliminate in this system?

3x - 2y = 12

2x + 2y = - 2

both

neither

Multiple Choice

Which variable is the easiest to eliminate in this system?

3x + 5y = - 15

- 3x - 4y = 30

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

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Find the best variable to solve for
Substitute the expression in the opposite equation and solve for the remaining variable
Use the value to find the missing one

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

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Solving Systems of Linear Equations

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