Solving a System of Equations in Two Variables By Graphing

Chapter 8.1

When graphing two equations there are 3 possible scenarios.

1. The two lines could intersect at 1 unique point.

•(-2, 4)

When graphing two equations there are 3 possible scenarios.

2. The two lines could be parallel and never intersect.

Inconsistent system of equations

No Solution

When graphing two equations there are 3 possible scenarios.

3. The two lines could be the same line (coincide).

Dependent equations

Infinite number of solutions

Graphing a system of equations

1. May have to rewrite each equation into y = mx + b.

2. Plot the points and draw each line.

3. Determine the solution.

y = mx + bx + y = 12

y = -x + 12

-x -x

m = -1, b = 12

-x + y = 4+x +xy = x + 4

m = 1, b = 4

1. Solve by graphing.

•m = -1, b = 12

m = 1, b = 4

•• •

(4, 8)

x + y = 12

-x + y = 4 •

x + y = 12

-x + y = 4

1. Solve by graphing.

lines intersect

-3 -3 -3

y = mx + b4x + 2y = 8

2y = -4x + 8

-4x -4x

2 2 2

y = -2x + 4

m = -2, b = 4

-6x – 3y = 6

-3y = 6x + 6

+6x +6x

y = -2x – 2

m = -2, b = -2

2. Solve by graphing.

x•

m = -2, b = 4

m = -2, b = -2 •

••

4x + 2y = 8

-6x – 3y = 6

•

•

4x + 2y = 8

-6x – 3y = 6No Solution

Inconsistent system of equations

2. Solve by graphing.

parallel lines

12 12 12

y = mx + b3x – 9y = 18

-9y = -3x + 18

-3x -3x

-9 -9 -9

y = x – 2

m = , b = -2

-4x + 12y = -24

12y = 4x – 24

+4x +4x

y = x – 2

m = , b = -2

3. Solve by graphing.

•

m = , b = -2

m = , b = -2•

3x – 9y = 18

-4x + 12y = -24

•Infinite number of solutions

Dependent equations

3x – 9y = 18

-4x + 12y = -24

3. Solve by graphing.

lines coincide

Solving a System of Equations in Two Variables By Graphing

Chapter 8.1