# How to Solve Linear Equations

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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)

 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

Example 2:   -7x – 3y =31              … (1)
9x – 5y = 41              … (2)

Solution: - From equation (1) we get
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