Solving Simultaneous Equations Using Bar Method
Simultaneous Equations
LO: to be able to represent and solve
simultaneous equations using the Bar
Method.
Using the bar method, solve
4x + y = 17
2x + y = 11
Draw a bar for each
equation
Compare the bars to try and
eliminate either x or y
Using the bar method, solve
4x + y = 17
2x + y = 11
The second bar matches
part of the first bar
11
Using the bar method, solve
4x + y = 17
2x + y = 11
Subtract it to find
the value of x
6
11
2x = 6
So x = 3
17 –
11
= 6
4x + y -
(2x + y)
= 2x
x = 3
Using the bar method, solve
4x + y = 17
2x + y = 11
Substitute the value
of x into one of the
original bars to find y
Subtract to find y
3
+ 3
= 6
6
y = 11 – 6
y = 5
x = 3
y = 5
Now try these. Using the bar method, solve:
1) 5x + 2y = 13
x + 2y = 9
2)
x + 3y = 9
x + y = 6
Challenge:
3) 2x + 3y = 19
6x + 2y = 22
Answers
1)
x = 1
y = 4
2)
x = 4.5
y = 1.5
3)
x = 2
y = 5
Using the bar method, solve
2x + y = 7
5x - y = 14
The y is subtracted from the
second bar to get 14
14
x
x
x
Combine the bars by
adding to eliminate y
Using the bar method, solve
2x + y = 7
5x - y = 14
The y is subtracted from the
second bar to get 14
14
x
x
x
Combine the bars by
adding to eliminate y
Using the bar method, solve
2x + y = 7
5x - y = 14
The y is subtracted from the
second bar to get 14
x
x
x
7 + 14 = 21
Combine the bars by
adding to eliminate y
2x + 5x + y
- y
= 7x
7x = 21
So
x = 3
x = 3
Using the bar method, solve
2x + y = 7
5x - y = 14
Substitute the value of x into
one of the original bars to
find y
x
x
x
7 + 14 = 21
Combine the bars by
adding to eliminate y
3 3
1
x = 3
3 + 3 = 6
7 – 6 = 1
So y = 1
y = 1
Learn how to represent and solve simultaneous equations using the Bar Method. Step-by-step illustrations show how to eliminate variables and find solutions. Practice with provided examples and a challenge problem to enhance your understanding.
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Presentation Transcript
Simultaneous Equations LO: to be able to represent and solve simultaneous equations using the Bar Method.
Using the bar method, solve 4x + y = 17 2x + y = 11 Draw a bar for each equation 17 y x x x x Compare the bars to try and eliminate either x or y 11 x x y
Using the bar method, solve 4x + y = 17 2x + y = 11 The second bar matches part of the first bar 17 y x x x x 11 11 x x x x y y
Using the bar method, solve 4x + y = 17 2x + y = 11 x = 3 Subtract it to find the value of x 17 y x x x x x x 4x + y - (2x + y) = 2x 17 11 = 6 x x y 11 6 2x = 6 So x = 3
Using the bar method, solve 4x + y = 17 2x + y = 11 x = 3 Substitute the value of x into one of the original bars to find y y = 5 17 y x x x x Subtract to find y 6 11 x x 3 = 6 y y = 11 6 y = 5 + 3
Now try these. Using the bar method, solve: 1) 5x + 2y = 13 x + 2y = 9 Answers 1) x = 1 y = 4 2) x + 3y = 9 x + y = 6 Challenge: 3) 2x + 3y = 19 6x + 2y = 22 2) x = 4.5 y = 1.5 3) x = 2 y = 5
Using the bar method, solve 2x + y = 7 5x - y = 14 The y is subtracted from the second bar to get 14 7 x x y x x x x x y 14 Combine the bars by adding to eliminate y
Using the bar method, solve 2x + y = 7 5x - y = 14 The y is subtracted from the second bar to get 14 11 x x x x y y x x x x x y 14 Combine the bars by adding to eliminate y
Using the bar method, solve 2x + y = 7 5x - y = 14 x = 3 The y is subtracted from the second bar to get 14 7 x x y 2x + 5x + y - y = 7x x x x x x x x y y 7 + 14 = 21 7x = 21 So x = 3 Combine the bars by adding to eliminate y
Using the bar method, solve 2x + y = 7 5x - y = 14 x = 3 y = 1 Substitute the value of x into one of the original bars to find y 3 + 3 = 6 7 6 = 1 So y = 1 3 3 1 7 x x y x x x x x x x y y 7 + 14 = 21 Combine the bars by adding to eliminate y
