1. 7.1 Solving Linear Systems by Graphing

2. System of 2 linear equations (in 2 variables x & y)
2 equations with 2 variables (x & y) each.
Ax + By = C
Dx + Ey = F
Solution of a System –
an ordered pair (x,y) that makes both eqns true.

3. Ex: Check whether the ordered pairs are solns. of the system
Ex: Check whether the ordered pairs are solns. of the system. x-3y= -5 -2x+3y=10
(-5,0)
-5-3(0)= -5
-5 = -5
-2(-5)+3(0)=10
10=10
Solution
(1,4)
1-3(4)= -5
1-12= -5
-11 = -5
*doesn’t work in the 1st eqn, no need to check the 2nd.
Not a solution.

4. Solving a System Graphically
Graph each equation on the same coordinate plane. (USE GRAPH PAPER!!!)
If the lines intersect: The point (ordered pair) where the lines intersect is the solution.
If the lines do not intersect:
They are the same line – infinitely many solutions (they have every point in common).
They are parallel lines – no solution (they share no common points).

5. Ex: Solve the system graphically. 2x-2y= -8 2x+2y=4
(-1,3)

6. Ex: Solve the system graphically. 2x+4y=12 x+2y=6
1st eqn:
x-int (6,0)
y-int (0,3)
2ND eqn:
What does this mean?
the 2 eqns are for the same line!
¸ many solutions

7. Ex: Solve graphically: x-y=5 2x-2y=9
1st eqn:
x-int (5,0)
y-int (0,-5)
2nd eqn:
x-int (9/2,0)
y-int (0,-9/2)
What do you notice about the lines?
They are parallel! Go ahead, check the slopes!
No solution!

8. Ex: Solve graphically y = 1/2x y = -3/4x + 5
1st eqn:
m = ½
b = 0
2nd eqn:
m = -3/4
b = 5
Graph!
Intersection?

9. Ex: Solve graphically y = -x – 3 2x – y = -3
1st eqn:
m = -1
b = -3
2nd eqn:
Leave in standard form or put in slope-intercept form?
Standard: x-int: (-3/2,0) and y-int: (0, 3)
Slope-int: m = 2 and b = 3
Graph!
Intersection?