Download Lesson 10: Simu Eqns - Elimination

Note 13: Simultaneous Equations
A pair of simultaneous equations gives
information about two unknown numbers. They
have to be solved together to give the two
solutions.
Method A: Elimination


Line the equations up vertically
Look for a variable that can easily be eliminated (or
can be multiplied by a factor to make a variable
eliminated)

Add the equations together eliminating a variable

Solve the equation to find the unknown variable

Substitute the variable found into an equation to
find the other variable
Example 1
Use elimination to
solve the equations
3x – y = 11........... (1)
x + y = 5 ............ (2)
Step 1 Each of the y terms has a 1 in front (one is
negative and the other is positive)
Step 2 Add the two equations together
3x – y = 11
+ x+y = 5
4x = 16
x=4
Step 3 Substitute x = 4 into EITHER equation to find y.
x+y =5
4+y =5
Ans (4 , 1)
y=1
Example 2
Use elimination to
solve the equations
3x – 2y = 21 ........... (1)
4x + 7y = – 1 ............ (2)
Step 1 We need to multiply BOTH equations by different
numbers to make a pair of x’s OR a pair of y’s with
the same number in front!
Step 2 Multiply (1) through by 7
21x – 14y = 147........(3)
Multiply (2) through by 2
8x + 14y = – 2 ........(4)
Step 3
Add and solve
3 x 5 – 2y = 21
y = -3
Ans (5 , -3)
29x = 145
x=5
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Exercise R