Solving Simultaneous Equation By Elimination Method

Solving Simultaneous Equation By Elimination

Method

3x+2y=6

5x - y= 8

In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other

3x+2y=6, 5x−y=8

5×3x+5×2y=5×6,3×5x+3(−1)y=3×8

Simplify

15x+10y=30,15x−3y=24

Subtract 15x−3y=24 from $15 x + 10 y = 30$ by subtracting like terms on each side of the equal sign

15x−15x+10y+3y=30−24

Cancel out 15x - 15x to get

10y+3y=30−24

Add $10 y$ to $3 y$

13y=30−24

Subtract 24 from 30 to get

13y= 6

Divide both side by 13

y=136

5x−136=8

5x=13110

Divide through by 5

x=1322

x=1322,y=136

Comments

How to find the nth term an Arithmetic progression

Question Find the number of terms in an Ap given that its first and last terms are a and 37a respectively and that its common difference is 4a. Solution nth term of AP Tn = a +(n-1)d From the question First term a = a Last term Tn = 37a Common difference d = 4a Number of terms n =? Substitute a, Tn and d into the nth term formula Tn = a +(n-1)d 37a = a +(n-1)4a Collect like terms 37a-a = (n-1)4a 36a = (n-1)4a Divide through by 4a 36a/4a = (n-1)4a/4a 9 = n-1 make n subject formula n = 9+1 n = 10 The AP as 10 terms

Arithmetic Progression

How to calculate the common difference when the first term and the nth term is know. Question: The 28th term of an AP is -5. Find the common difference if its first term is 31. Solution T1 = a ( First term of the sequence) a = 31 T28 = -5 (28th term of the sequence) d = ? (common difference) Recall the nth term formula of Ap i.e Tn = a + (n-1)d Substitute 28 for n to get the following equation T28 = a + (28-1)d T28 = a + 27d Substitute T28 for -5 and 31 for a in the equation above -5 = 31 + 27d Subtract 31 from both sides of the equation -5 -31 = 27d -36 = 27d Divide through by 27 -36/27 = 27d/27 ...

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