Solving Linear Equations Presentation

Solving Linear Equations Using Graphing Substitution and Elimination Need some homework help? Go to: http://go.hrw.com Keyword: MA1 Homework Help

What’s the Deal? ,[object Object],[object Object]

Three Parts ,[object Object],[object Object],[object Object]

Solving for linear equations answers the question: ,[object Object],[object Object]

Remember - Slope intercept form: y = mx + b ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

If the slope is ½ ,[object Object],[object Object],[object Object],[object Object]

Graphing Systems of equations ,[object Object],[object Object],[object Object],[object Object]

Graph y=3x + 1 ,[object Object],[object Object]

Let’s add y = -x + 5 The slope is -1. Or down one And right one.

The coordinates of the intersecting point is your solution. The lines intercept at (1, 4) so the solution is x=1, y =4. The lines intercept at (1, 4) so the solution is x=1, y =4.

Solve by graphing ,[object Object],[object Object],[object Object]

The coordinates of the intersecting point is your solution. The lines intercept at (-20,-12) so the solution is x= -20, y = -12.

Now solve equations in standard form. ,[object Object],[object Object],[object Object],[object Object]

Change 3x + 2y = -6 to y-intercept form ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Subtract -3x from both sides

Change -3x + 2y = 6 to y-intercept form ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Add 3x to both sides

Graph the equations: y = - 3 / 2 x -3 and y = 3 / 2 x + 3 x = 2, y = 0 The solution is (2,0)

Part Two – Solve linear equations by substitution Need Help? Go online to go.hrw.com See your textbook’s “internet connect” notes

Here’s what will happen ,[object Object],[object Object],[object Object],[object Object]

Solve for the following equations. ,[object Object],[object Object],[object Object],[object Object],[object Object]

Step 2) Insert the isolated value into the equation, this allows you to solve for one variable at a time. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Careful! You are only half done. You still have to solve for the other variable!

Solve for: 2x + 8y = 1 and x = 2y ,[object Object],[object Object],[object Object],[object Object],[object Object],The solution is (1/6, 1/12)

Try one. ,[object Object],[object Object]

x is given as 7. Insert 7 for any occurrence of x to solve for y. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Solve for x and y. 3x + y = 4 and 5x – 7y = 11 ,[object Object],[object Object],[object Object],[object Object]

Subtract 3x from both sides to isolate y. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

The Distributive Property is used. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Continuing… ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

3( 3 / 2 ) + y = 4 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Part Three – Solving equations by Elimination Need some homework help? Go to: http:// go.hrw.com Keyword: MA1 Homework Help

Solve using substitution after manipulating equations in standard form. ,[object Object],[object Object],[object Object],[object Object]

Let’s solve by elimination. ,[object Object],[object Object],[object Object],[object Object]

2x + 3y = 21 -3x – 3y = -12 ,[object Object],[object Object],[object Object]

The steps and explanations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

2x + 3y = 21 -3x – 3y = -12 You may pick either one. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Try One. ,[object Object],[object Object]

Eliminate the x values. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

4x = 21 / 9 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Ready to go one more step? ,[object Object],[object Object]

Let’s try 11x + 2y = -8 and 8x + 3y = 5 ,[object Object],[object Object],[object Object]

Multiply both sides ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Results of the First Steps ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

-17x = 34, x = -2 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

One more for practice ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

One more for practice ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Which way of solving works best for you? ,[object Object],[object Object],[object Object],[object Object]

You have reviewed the first three parts of Chapter 7.

Solving Linear Equations Presentation

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Solving Linear Equations Presentation