Solve the following pair of linear equations by the substitution metho

1.	Solve the following pair of linear equations by the substitution method.(i) x + y = 14x – y = 4(ii) 3x – y = 39x – 3y = 9
Answer» ⠀⠀ıllıllı uoᴉʇnloS ıllıllı $\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$ (i) Given: x + y = 14 and x - y = 4 are the two equations. From 1st EQUATION, we get: x = 14 - y Now, put the VALUE of x in second equation to get, (14 - y) - y = 4 ➠ 14 - 2y = 4 ➠ 2y = 10 ➠ Or y = 5 By the value of y, we can now FIND the exact value of x; ∵ x = 14 - y ∴ x = 14 - 5 Or x = 9 Hence, x = 9 and y = 5. $\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$ (ii) Given: 3x - y = 3 and 9x - 3y = 9 are the two equations. From 1st equation, we get, x = (3 + y)/3 Now, substitute the value of x in the given second equation to get, 9(3 + y)/3 - 3y = 9 ➠ 3(3 + y) - 3y = 9 ➠ 9 + 3y - 3y = 9 ➠ 9 = 9 Therefore, y has infinite values and since, x = (3 + y)/3, so x also has infinite values. $\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

Solve the following pair of linear equations by the substitution method.(i) x + y = 14x – y = 4(ii) 3x – y = 39x – 3y = 9

Answer»

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(i) Given:

x + y = 14 and x - y = 4 are the two equations.

From 1st EQUATION, we get:

Now, put the VALUE of x in second equation to get,

(14 - y) - y = 4

➠ 14 - 2y = 4

➠ 2y = 10

➠ Or y = 5

By the value of y, we can now FIND the exact value of x;

∵ x = 14 - y

∴ x = 14 - 5

Or x = 9

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(ii) Given:

3x - y = 3 and 9x - 3y = 9 are the two equations.

From 1st equation, we get,

Now, substitute the value of x in the given second equation to get,

9(3 + y)/3 - 3y = 9

➠ 3(3 + y) - 3y = 9

➠ 9 + 3y - 3y = 9

➠ 9 = 9

Therefore, y has infinite values and since, x = (3 + y)/3, so x also has infinite values.

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