Secondary 2 Mathematics-Simultaneous Linear Equation in 2 Unknowns Worked Examples

Examples

Example 1

  5x+4y=43  2x+y=13

• Solution=3,y=7

Elimination Method

  2(5x+4y)=43=10x+8y=86  5(2x+y)=13=10x+5y=65  (10x+8y)-(10x+5y)=3y=21  Y=21/3=7  13-(7)=6  X=6/2=3

Substitution Method

  Y=13-2x  5x+4(13-2x)=43  5x+52-8x=43  -3x+52=43  3x=52-43=9  X=9/3=3  Y=13-2(3)=7

Graph Method

X 1 2 3 4 5y 9.5 8.25 7 5.75 4.5

  5x+4y=43

  2x+y=13X 1 2 3 4 5y 11 9 7 5 3

Example 2

  5x-5y=7  6x-6y=12

• No Solution

Elimination Method

  6(5x-5y)=30x-30y=42  5(6x-6y)=30x-30y=60  (30x-30y)-(30x-30y)=0=18

Substitution Method

  X=7+5y/5  6(7+5y/5)-6y=12  42+30y-30y=60  42=60

Graph Method

  5x-5y=7

  6x-6y=12

X 1 2 3 4 5y -0.4 0.6 1.6 2.6 3.6

X 1 2 3 4 5y -1 0 1 2 3

Example 3

  4x+8y=24  7x+14y=42

• Infinitely Many Solutions

Elimination Method

  7(4x+8y)-4(7x+14y)=28x+56y-28x-56y=0

Substitution Method

  X=24-8y/4  7(24-8y/4)+14y=42  168-56y+56y=168  168=168

Graph Method

• 4x+8y=42

• 7x+14y=42

X 1 2 3 4 5y 4.75 4.25 3.75 3.25 2.75

X 1 2 3 4 5y 4.75 4.25 3.75 3.25 2.75

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