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Linear Equations in Two Variables
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Linear Equations in Two Variables

Equations of the form ax + by = c and bx + ay = d where a b
To solve the above type of equations, the following algorithm may be used.
STEP I Obtain the two equations.
Let the equation be ax + by - c and bx + ay = d.
STEP II Adding and subtracting the two equations, we obtain
(a + b)x + (a + b)y = c + d x + y = (c + d) / (a + b) ...(i)
(a - b)x - (a - b)y = c - d x - y = (c - d) / (a - b) ...(ii)
STEP III Add and subtract equations (i) and (ii) to get the values of x and y.
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Example : Solve: 12x + 10y = 76
10x + 12y = 34
Solution: You have ,
12x + 10y = 76 ...(i)
10x + 12y = 34 ...(ii)
Adding equations (i) and (ii), you will get
22x + 22y = 110 x + y = 5 ...(iii)
Subtracting equation (ii) from equation (i), you will get
2x - 2y = 42 x - y = 21 ...(iv)
Adding equations (iii) and (iv), you will get
2x = 26 x = 13
Putting x = 13 in equation (iii), you will get y = -8.
Hence, x = 3 and y = -8 is the solution of the given system of equations.
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