Simultaneous Linear Equations

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Simultaneous Linear Equations!

• By Pollie Deeks and
• Grace Gulliford

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Learning summary

• After studying this section, you will
• be able to
• Solve simultaneous linear equations by
  elimination
• Solve simultaneous linear equations by
  substitution
• Complete a process check!

Each page click on here to get back to learning
summary!
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Solving Simultaneous Linear Equations(By
Elimination)

• Two equation in two unknown can have a unique
  solution.
• The first solution well be focusing on is
  elimination

Example Solve x2y 7 4x-3y 6 4x8y 28 4x-3y
6 11y 22 y 2 x2x2 7 x 3 The solution is x3,
y 2
The object is to make either the x terms the
same or the y terms the same. Multiply the first
equation by 4.
Subtract the second equation from your new
equation
Divide each side by 11
Substitute for y in the first equation
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Solving Simultaneous Linear Equations (By
Substitution)

• The simultaneous equations can also be solved by
  writing
• one of the equations in the form x or y.
  This is the
• second method and it is called substitution.

Example Solve 2x-3y 7 4xy 0 y-4x 2x-3(-4x)
7 2x12x 7 14x 7 x ½ y-4x ½ -2 The solution
is x ½, y-2
Write the second equation in the form y
Substitute for y in first equation and solve for
x.
Substitute for x in second equation
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Progress Check!

• Solve these pairs of simultaneous equations
• x2y 1, 2xy 5
• x2y 6, 2x-6y 12
• 3x-2y-9, 4x5y-½
• Answers

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Answers

• x3 y-1
• x 5 y ½
• x-2 y 1 ½