1. Solving Using the Substitution Method
Simultaneous Equations by Substitution
28-Mar-17
Solving Using the Substitution Method
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2. y x x = 3 y = 6 Solve with a graph y = x + 3 y = 2x x y x y 1 2 3 4 57 y x 1 2 3 4 5 6 7 8
–7 –6 –5 –4 –3 –2 –1 -1 -2 -3 -4 -5 -6 x 1 2 3 4 y 6 8
x = 3
y = 6
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3. Now put the value x = 3 into either of the two original equations to find the value of y
y = x + 3 (1)
y = 3 + 3
y = 6
Solve, by substitution:
y = x (1)
y = 2x (2)
Substitute the y in equation (1) with the 2x from equation (2) to obtain equation (3)
2x = x (3)
2x – x = 3
x = 3
x = 3
y = 6
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4. 1. y = x + 4 4. y = 2x + 1 y = 2x y = 3x 2. y = 2x + 7 5. y = x + 5
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5. 1. y = x + 4 4. y = 2x + 1 y = 2x y = 3x x = 4 and y = 8
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6. Choose the pair with a sum of 5
y = x2 + 2x – 8
y = 6 – 3x
1 x –14 = -14
2 x – 7 = -14
7 x – 2 = -14
14 x –1 = -14
Choose the pair with a sum of 5
= 5
7 – 2 = 5
6 – 3x = x2 + 2x – 8
0 = x2 + 2x + 3x – 8 – 6
0 = x2 + 5x – 14
0 = (x + 7)(x – 2)
x = -7 and +2
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7. 1. y = x2 + 8x + 12
y = x2 – 4x – 7
y = x
y = 3 – x
2. y = x2 + 8x + 10
y = x2 – 5x – 35
y = 3x
y = 2x – 5
y = x2 – 5x – 5
6. y = x2 + x
y = 1 – 4x
y = x2 + 25
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8. 1. y = x2 + 8x + 12 y = x2 – 4x – 7 y = x y = 3 – x x = -3 and -4
© Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09