2 1 1 2 - medelgado.com · 5-1 System of Equations - Solve by Graphing.notebook December 09, 2015....
Transcript of 2 1 1 2 - medelgado.com · 5-1 System of Equations - Solve by Graphing.notebook December 09, 2015....
5-1 System of Equations - Solve by Graphing.notebook December 09, 2015
1
Ex 1:
5-1 Solve System of Equations by Graphing
Determine if (1,2) is a solution of the given system of equations:
y = x + 12x + y = 4
Do these equations (lines) cross at point (1,2)?
Step 1: Plug (1,2) into both equations. If bothbalance, then point (1,2) is a solution.
Point (1,2) is a solution because both balance when you plug in (1,2). Both lines cross at (1,2).
y = x + 1 2x + y = 4
2 1 212 = 1 + 1
2 = 2
2(1) + 2 = 4
2 + 2 = 4
4 = 4
ANSWER
5-1 System of Equations - Solve by Graphing.notebook May 13, 2016
5-1 Solve System of Equations by Graphing
Checks for Example 1
1) Determine if (-3, 2) is a solution of the given system of equations:
a + b = -1b + 3a = 4
Step 1: Plug (-3, 2) into both equations.
a + b = -1 b + 3a = 4
+ 2 = -1
= -1
2 + 3(-3) = 4
2 + -9 = 4 2 - 9 = 4
-7 = 4
Not a solution because both equations do not balance.
ANSWER
2) Determine if (2, -3) is a solution of the given system of equations:
2x + y = 1
x = 2y + 8
Step 1: Plug (2, -3) into both equations.
2x + y = 1x = 2y + 8
2 = 2(-3) + 8
2 = -6 + 8
2 = 2
2(2) + (-3) = 1
4 + (-3) = 1
4 - 3 = 11 = 1
Point (2, -3) is a solution. Both lines cross at (2, -3).
3) Determine if (20, 40) is a solution of the given system of equations:
a = b + 10
b - a = -20
1 4
a = b + 10 1 4 b - a = -20
20 = (40) + 10 1 4
40 1( )
40 4
20 = + 10 1 4
20 = + 10
20 = 10 + 10
20 = 20
40 - 20 = -20
20 = -20
Not a solution because both equations do not balance.
ANSWER
ANSWER
5-1 System of Equations - Solve by Graphing.notebook December 09, 2015
Ex 2:Solve by graphing.
Where do these two lines cross???
y = x + 3 1 2
5y = x - 3
Step 1: Graph each line using slope (m) & y-intercept (b).
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
x
y
5y = x - 3y = x + 3 1 2
ANSWER (2, 2)Both lines intersect at (2,2).
m =
b = 3
1 2
5m =
b = -3
5-1 Solve System of Equations by Graphing 3
5-1 System of Equations - Solve by Graphing.notebook December 09, 2015
Ex 3:
5-1 Solve System of Equations by Graphing
Solve by graphing.Where do these two lines cross???
x + y = -42x - 3y = -3
Step 1: Solve both equations for y. 2x - 3y = -3x + y = -4
-x -xy = -x - 4
-2x -2x- 3y = -2x - 3
-3 -3 -3
y = x + 1 2 3
Step 2: Graph each line using slope (m) & y-intercept (b).
y = x + 1 2 3
y = -x - 4
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
x
y
ANSWER (-3, -1)Both lines intersect at (-3,-1).
m = -1
b = -4
m =
b = 1
2
5-1 System of Equations - Solve by Graphing.notebook December 09, 2015
5-1 Solve System of Equations by Graphing
Checks for Examples 2 & 3:Solve by graphing.Where do these two lines cross???
2x - y = -13x + y = -4
Step 1:
Step 2: Graph each line using slope (m) & y-intercept (b).
2x - y = -1 3x + y = -4-2x -2x
- y = -2x - 1-1 -1 -1
y = 2x + 1
-3x -3x
y = -3x - 4
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
x
y
ANSWER (-1, -1) Both lines intersect at (-1,-1).
m =
b = 1
m =
b = -4
y = 2x + 1 y = -3x - 4
2 1
3 1