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