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