Solving Linear Equations UsingGraphingSubstitution

andElimination

Introduction to Unit Six

What’s the Deal?

• There are a number of ways to solve groups of linear equations.

• In this lesson, we will find points on a coordinate plane that solve linear equations in standard form and y-intercept form.

Three Parts(over the next few days)

• Part One – Solve linear equations by graphing.

• Part Two – Solve linear equations by substitution.

• Part Three – Solve linear equations by elimination.

Solving for linear equations answers the question:

• What values of x and y fit into both equations?

• The answer is usually given in (x,y) format (ie. (-4, 6) or (3,8).

Remember - Slope intercept form: y = mx + b

• m = slope• b = y-intercept

• In y = 1/2x – 7, – What is the y-intercept?– What is the slope?

• Rise over Run– Rise = up, or plus one (+1)– Run = right, or plus two (+2).

If the slope is ½

Rise

Run = slope = m

The rise is 1 and the run is 2.

From the origin (0,0), go up 1 and right 2.

Graphing Systems of equations

• y = 3x + 1

• y = -x + 5

• Since both are in y-intercept format (y=mx+b) find the point through which the line intercepts the y-axis.

• Graph these equations. Answers on the next slides.

Graph on the board

Graphy = 3x + 1y = -x + 5

Graphsy = 3x + 1y = -x + 5

Solving By Graphing

Which point or points can fit into both equations?

The result is the ( x,y ) coordinates of the intersection.

The lines inter-cept at (1, 4) sothe solution isx=1, y =4.

The lines inter-cept at (1, 4) sothe solution isx=1, y =4.

The coordinates of the intersecting point is your solution.

Solve by graphing

• y = x +3

• y = x +1

• The next two slides will show the solution.

3

4

2

3

The lines inter-cept at (-20,-12) sothe solution isx= -20, y = -12.

The coordinates of the intersecting point is your solution.

Now solve equations in standard form.

• 3 x + 2y = -6 and

• -3 x + 2y = 6

• Step One: Convert equations from standard form to y-intercept form.

• Let’s review that from a previous lesson using the equations above…

Change 3x + 2y = -6to y-intercept form

3x + 2y = -6

-3x -3x

-2y = -3x - 6

Now we need to get y isolated. In this case, let’s divide both sides by 2.

2y = -3x - 6

2 2 2

Now simplify. y = - x -3

Subtract -3x from both sides

3

2

Change -3x + 2y = 6to y-intercept form

-3x + 2y = +6

+3x 3x

2y = 3x + 6

Get y isolated. Divide both sides by 2.

2y = 3x + 6

2 2 2

Now simplify. y = 3/2x + 3

Add 3x to both sides

Graph the equations:y = -3/2x -3

and y = 3/2x + 3

x = 2, y = 0The solution is(2,0)

Math is NOT a Spectator Sport

Write it Out!

End of Part One

Assignment:pg. 323-4: 10 - 27

Extras for presentation

x y-4-2 0+2+4

-6 -4 -2 0 +2 +4 +6