Warm-Up1. Put in slope-intercept form:

3x – 4y = -12

2. Graph the line: y = -1/2 x + 3

-6 -4 -2 2 4 6

-6

-4

-2

2

4

6

Daily Essential Question:

Why would I use the graphing method to solve a system of linear equations?

System of 2 linear equations:

2 linear equations graphed on the same coordinate plane

Solution of a System – › An ordered pair, (x,y) where the 2 lines

intersect› An ordered pair, (x,y) that makes both

equations true

Solving a System Graphically

1. Graph each equation on the same coordinate plane.

2. If the lines intersect: The point (ordered pair) where the lines intersect is the solution.

3. Do lines always intersect?4. What if the lines don’t intersect? Would they

have a solution?5. Do we have a name for lines that will never

intersect? What is it?6. So, if lines are ________, they have ____

solution. parallel

no

y = 3x – 12

.......

.......

The coordinates of the point

of intersection

is the solution

1. Solve the system graphically:

y = -2x + 3

How can we prove that our answer is correct?

y = 3x – 12

y = -2x + 3

Solution: (3, -3)

x y

y = 3x – 12-3 = 3(3) – 12

-3 = 9 – 12

-3 = -3

y = -2x + 3-3 = -2(3) + 3

-3 = -6 + 3

-3 = -3

We are correct!

2. Solve the system graphically:

-6 -4 -2 2 4 6

-6

-4

-2

2

4

6

.......

..

..

The coordinates of the point

of intersection

is the solution

y = - x – 2

y = 2/3 x + 3

.

How can we prove that our answer is correct?y = - x – 2

y = 2/3 x + 3

Solution: (-3, 1)

x y

y = - x – 2

1 = - (-3) – 21 = -1(-3) – 21 = 3 – 2

1 = 1

y = 2/3 x + 31 = 2/3 (-3) + 31 = 2/3 (-3/1) + 31 = -6/3 + 3

1 = -2 + 3

1 = 1

We got it right!

3. Solve the system graphically:

-6 -4 -2 2 4 6

-6

-4

-2

2

4

6.y = x + 4

y = -x + 2 ......

.

.....

.The coordinates of the point of intersection is the solution

y = x + 43 = -1 + 4

y = -x + 23 = -(-1) + 2

We did it!

4. Solve graphically:

y x 5 y x 5

-6 -4 -2 2 4 6

-6

-4

-2

2

4

6

....

...

x – y = 5

2x + 2y = 10 ........

The coordinates of the point of

intersection is the solution

x – y = 5

5 – 0 = 5

2x + 2y = 10 2(5) + 2(5)=10

Dang, we’re good!

What if we want to make sure the coordinates really are the solution without graphing….how could we figure that out?

Any ideas?

Example: Someone says that the solution to the system below is (1, 4). How could we find out if the answer is correct?

x - 3y = -5 -2x + 3y = 10

Check whether the ordered pairs are solutions of the system:

A. (1,4) 1-3(4)= -51-12= -5-11 = -5*doesn’t work in the 1st

equation, no need to check the 2nd.

Not a solution.

B. (-5,0)

-5-3(0)= -5-5 = -5

-2(-5)+3(0)=1010=10

Solution

x - 3y = -5 -2x + 3y = 10x y x y