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Let us take a mathematical problem to indicate the necessary steps to solve the linear equations:

**Example 1**: -

3x – 2y = 2 … (1)

7x + 3y = 43 … (2)

3x – 2y = 2 … (1)

7x + 3y = 43 … (2)

Instruction |
Method of solution |

a) From equation (1), express x in terms of y. likewise, from equation (2), express x in terms of y. |
From equation (1): 3x=2y+2 So, x=(2y+2)/3 … (3) From equation (2) 7x=-3y+43 x= (-3y+43)/7 … (4) |

b) Evaluate the values of x in (3) and (4) forming the equation in y. |
From equation (3) and (4), we get, (2y+2)/3=(-3y+43)/7 … (5) |

c) Solve the linear equation (5) in y |
Simplifying, we get 14y+14=-9y+129 23y=115 y=5 |

d) Putting the values of y in (3) or (4), find the value of x |
Putting the value of y in equation (3) we get x=(2*5 +2)/3=4 |

e) Required solution of the two equations |
Therefore x=4 And y =5 |

9x – 5y = 41 … (2)

7x = 31+3y

x= (31+3y)/7 … (3)

Similarly from equation (2) we get,

9x = 41 + 5y

x = (41 + 5y) / 9 …(4)

From equations (3) and (4)

(31 + 3y) / 7 = (41 + 5y) /9

9(31 + 3y) = 7(41+5y)

279 +27y = 287+35 y

8y = -8

y = -1

Putting the value of y = -1 in equation (3) we get,

x=(31-3)/7=28/7=4

Therefore x =4 and y = -1