3.1 System of Equations Solve by graphing. Ex 1) x + y = 3 5x – y = -27 Which one is the solution of this system? (1,2) or (-4,7) *Check (1,2)Check (-4,7)

3.1 System of Equations

Solve by graphing

Ex 1) x + y = 3

5x – y = -27

Which one is the solution of this system? (1,2) or (-4,7)

*Check (1,2) Check (-4,7)

Is 1 + 2 ? 3 Is -4 + 7 ? 3

3 = 3 yes 3 = 3 yes

Is 5·1-2 ? -27 Is 5·(-4)-7 ? -27

5 - 2 ? -27 -20 – 7 ? -27

-3 = -27 no -27 = -27 yes

So (1,2) is not the So (-4,7) is the solution

Solution of the system

Solve by Graphing

Ex 1) y – x = 1

y + x = 3

y = x + 1

y = -x + 3

Therefore the solution

of this system is (1,2)

(1,2)

Solve by Graphing

Ex 1) y = -3x + 5

y = -3x - 2

The lines are parallel,

so there is no solution

for this system of

equations

Solve by Graphing

Ex 1) 3y – 2x = 6

-12y + 8x = -24

3y = 2x + 6

-12y = -8x - 24

y = 2/3 x + 2

y = 2/3 x + 2 There are infinite

numbers of solution because the lines are coinciding

• A system of equations is consistent if they have at least one solution

• A system of equation is inconsistent if they have no solution

• A system of equations is dependent if it has many solutions

• A system of equations is independent if it has one solution or no solutions

***When an equation in a system can be obtained by multiplying both sides of another equation by a constant, the two equations are said to be dependent

Example

Y = -2

X = 2

What is the solution? Dependent or independent? Consistent or Inconsistent?

Answer: (2, -2), consistent, independent

Example

6x – 2y = 2

9x – 3y = 1


Answer: No solution; inconsistent, independent

Example

Y = 3 - x

2x +2y = 6


Answer: Infinite many solutions; consistent, dependent

Example

Y = 4 - x

Y = x - 4


Answer: (4,0) consistent, independent

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3.1 System of Equations Solve by graphing. Ex 1) x + y = 3 5x – y = -27 Which one is the solution of this system? (1,2) or (-4,7) *Check (1,2)Check (-4,7)