Ch 7: System of Equations

E) Parallel & Same Lines

Objective:

To identify the number of solutions of a system of linear equations.

Intersection: Parallel: Coincidental

Definitions

Lines cross at one point only

Lines never cross Same line – crosses at every point

One solution No solutionInfinitely many

solutions

x = ___, y = ____ False statement True Statement

y –2 x 5y –2 x 1

Example 1

y –2 x 5y –2 x 1–( )0 = 0 + 4

False!

No solution

Graphing Elimination

−

Example 2

-2x + y 3−4x + 2y 6

2( )

0 + 0 = 0True!

Infinite solutions

Graphing Elimination

– 2x y 3– 4x 2y 6

LCM (x) = 4

−4x + 2y 6Same Line –

− −

Example 3

− x + 2y 34y = 2x + 8

2( )

0 + 0 = -2False!

No solution

Graphing Elimination

LCM (x) = 2

–

€

−x + 2y = 3

4y = 2x + 8

⎧ ⎨ ⎩

Line upLike Terms

−x + 2y 3−2x + 4y = 6−2x + 4y = 8− −

Example 4

Graphing

3y = x + 6 2x – 6y -12

3y = x + 62x – 6y = -12

2( )

0 + 0 = 0True!

Infinite solutions

Elimination

LCM (x) = 2

+

Line upLike Terms

-x + 3y 6 2x – 6y = -12

-2x + 6y = 12

Classwork

y = x + 4 y = x – 3

No solution

1) x + y = -3 -2x – 2y = 6

2)

Infinite solutions

Solve each system by Graphing

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x

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y

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x

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y

9x – 2y = 6-9x + 2y = -6

Infinite solutions

3) 4x + 6y = -2 -4x – 6y = 12

4)

6x + 7y = 66x + 7y = -7

5) 4x + 8y = -128x + 16y = -24

6)

No solution

No solution Infinite solutions

Solve each system using Elimination