Secondary 2 Mathematics-Simultaneous Linear Equation in 2 Unknowns Worked 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 5
y 9.5 8.25 7 5.75 4.5
 5x+4y=43
 2x+y=13
X 1 2 3 4 5
y 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 5
y -0.4 0.6 1.6 2.6 3.6
X 1 2 3 4 5
y -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 5
y 4.75 4.25 3.75 3.25 2.75
X 1 2 3 4 5
y 4.75 4.25 3.75 3.25 2.75

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