Question

Solve the pair of linear equation 7x+11y-3=0 and 8x+y-15=0 by substitution method

Answer 1

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Answer 2

Concept: A system of simultaneous linear equations is any pair of linear equations or more that have the same unknown variables in common. To solve such a system, one must identify values for the unknown variables that simultaneously satisfy each of the equations.

Given: simultaneous linear equations

7x + 11y -3 = 0 -------(i)

8x + y - 15 = 0--------(ii)

To find: values of x and y by substitution method

Solution:

The given simultaneous linear equations are

7x + 11y -3 = 0 -------(i)

8x + y - 15 = 0--------(ii)

equation (i) and (ii) can be written as

7x + 11y = 3 ------(*)

8x + y = 15-------(**)

From (*), 7x = 3 - 11y

                x = $\frac{3-11y}{7}$

Now substituting the value of x in equation (**), we get

$8(\frac{3-11y}{7} ) + y = 15\\\\\frac{24-88y}{7} +y = 15\\\\\frac{24-88y+7y}{7} = 15\\\\24-81y = 15*7\\\\24-81y = 105\\\\-81y = 105-24\\\\-81y = 81\\\\y = -1$

Substituting the value of y in (**), we get

$8x -1 = 15\\\\8x = 15+1\\\\8x =16\\\\x =2$

hence the value of x = 2 and y = -1.

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